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statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. In certain chi-square tests, one rejects
Minimum_chi-square_estimation
Evaluates how likely it is that any difference between data sets arose by chance
minimizing the chi-squared statistic. More generally however, when maximum likelihood estimation does not coincide with minimum chi-squared estimation, the distribution
Pearson's_chi-squared_test
Statistical hypothesis test
Chi-squared test nomogram Cramér's V GEH statistic G-test Minimum chi-square estimation Nonparametric statistics Wald test Wilson score interval "Chi-Square
Chi-squared_test
Method for fitting a statistical model to data
ordinary least squares can be thought of as special cases of minimum-distance estimation. While consistent and asymptotically normal, minimum-distance estimators
Minimum-distance_estimation
Approximation method in statistics
October 2023. van de Geer, Sara (June 1987). "A New Approach to Least-Squares Estimation, with Applications". Annals of Statistics. 15 (2): 587–602. doi:10
Least_squares
Interval bounded by an upper and a lower limit statistics
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a (sample) parameter of interest. This is in
Interval_estimation
Parameter estimation via sample statistics
In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate, since it identifies a point rather
Point_estimation
(clinical trials) Minimum chi-square estimation Minimum distance estimation Minimum mean square error Minimum-variance unbiased estimator Minimum viable population
List_of_statistics_articles
Measure of the error of an estimator
error Mean square quantization error Reduced chi-squared statistic Mean squared displacement Mean squared prediction error Minimum mean square error Overfitting
Mean_squared_error
Statistical property
Rao–Blackwell procedure for mean-unbiased estimation but for a larger class of loss-functions. Any minimum-variance mean-unbiased estimator minimizes
Bias_of_an_estimator
Branch of statistics
is the uniform distribution, then MAP estimation is equivalent to maximum likelihood estimation. Uniformly minimum-variance unbiased estimators (UMVUE)
Parametric_statistics
Procedure to estimate standard deviation from a sample
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Statistical test used on paired nominal data
2 {\displaystyle \chi ^{2}} has a chi-squared distribution with 1 degree of freedom. If the χ 2 {\displaystyle \chi ^{2}} result is significant, this
McNemar's_test
Concept in statistics
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method
Kernel_density_estimation
Unbiased statistical estimator minimizing variance
minimum mean square error (MMSE). An efficient estimator need not exist, but if it does and if it is unbiased, it is the MVUE. Since the mean squared
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Least squares approximation of linear functions to data
This special case of GLS is called "weighted least squares". The GLS solution to an estimation problem is β ^ = ( X T Ω − 1 X ) − 1 X T Ω − 1 y , {\displaystyle
Linear_least_squares
Method for estimating the unknown parameters in a linear regression model
uncorrelated. Under these conditions, the method of OLS provides minimum-variance mean-unbiased estimation when the errors have finite variances. Under the additional
Ordinary_least_squares
Statistical modeling method
least squares method is the same as the result of the maximum likelihood estimation method. Ridge regression and other forms of penalized estimation, such
Linear_regression
Form of causal modeling that fit networks of constructs to data
maximum likelihood estimation (MLE), full information maximum likelihood (FIML), ordinary least squares (OLS), weighted least squares (WLS), diagonally
Structural_equation_modeling
Statistical measure of association
Cramér's V is computed by taking the square root of the chi-squared statistic divided by the sample size and the minimum dimension minus 1: V = φ 2 min (
Cramér's_V
Statistical model for a binary dependent variable
Using the chi-squared test, we may then estimate how many of these permuted sets of yk will yield a minimum error less than or equal to the minimum error
Logistic_regression
Signal processing technique
statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the
Spectral_density_estimation
Danish statistician (1878–1939)
produced an influential paper in the journal Biometrika on minimum chi-squared estimation of the correlation coefficient. Disagreements about aspects
Kirstine_Smith
Statistical methods for comparing samples
sample-size for a minimum-detectable-effect calculations. The test is related to other well known tests such as Pearson's chi-squared test, Fisher's exact
Two-proportion_Z-test
Method of estimating the parameters of a statistical model, given observations
using a chi-squared distribution Generalized method of moments: methods related to the likelihood equation in maximum likelihood estimation M-estimator:
Maximum_likelihood_estimation
Data analysis approach in frequentist statistics
Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning
Estimation_statistics
Estimator for quality of a statistical model
model with minimum AIC is equivalent to selecting the model with minimum RSS—which is the usual objective of model selection based on least squares. Leave-one-out
Akaike_information_criterion
Measure of variation in statistics
of uncertainty Percentile Raw data Reduced chi-squared statistic Robust standard deviation Root mean square Sample size Samuelson's inequality Six Sigma
Standard_deviation
Statistical test
RVR')} Recalling that a quadratic form of normal distribution has a Chi-squared distribution: n ( R θ ^ n − r ) ′ [ R V R ′ ] − 1 n ( R θ ^ n − r ) →
Wald_test
Indian statistician (1915–1996)
the sum of chi-squares", Sankhya, 7 (1945), 27 - 28. In this paper, an expression of the distribution function of sum two dependent Chi-square random variables
Anil_Kumar_Bhattacharyya
Indicator for how well data points fit a line or curve
Gwowen (2008-04-01). "Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient". Organizational
Coefficient_of_determination
Study of high-dimensional data
deterioration in estimation performance in high dimensions observed in the previous paragraph is not limited to the ordinary least squares estimator. In
High-dimensional_statistics
Statistical regression where the dependent variable can take only two values
^{-1}({\hat {p}}_{t}){\big )}}}} Then Berkson's minimum chi-square estimator is a generalized least squares estimator in a regression of Φ − 1 ( p ^ t )
Probit_model
Specialized form of regression analysis, in statistics
process as the rest of the data, least squares estimation is inefficient and can be biased. Because the least squares predictions are dragged towards the
Robust_regression
Number of values in the final calculation of a statistic that are free to vary
associated with the squared lengths (or "sum of squares" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Statistical measure of how far values spread from their average
}}},\end{aligned}}} where ymin is the minimum of the sample. The F-test of equality of variances and the chi square tests are adequate when the sample is
Variance
Mathematical problem
orthogonal Latin squares is Graeco-Latin square, introduced by Euler. A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Statistical measure of the magnitude of a phenomenon
square root of the chi-squared statistic divided by the sample size. Similarly, Cramér's V is computed by taking the square root of the chi-squared statistic
Effect_size
Graphical representation of the distribution of numerical data
density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable
Histogram
Statistical property
term "standard error" can also be used to refer to the square root of the reduced chi-squared statistic in addition to the more common use in describing
Standard_error
Periodicity computation method
..122..879K. doi:10.1039/a700902j. Palmer, David M. (2009). "A Fast Chi-squared Technique For Period Search of Irregularly Sampled Data". The Astrophysical
Least-squares spectral analysis
Least-squares_spectral_analysis
Statistical property
non-linear transformations of the X variables). Apply a weighted least squares estimation method, in which OLS is applied to transformed or weighted values
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistics concept
a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate
Estimation of covariance matrices
Estimation_of_covariance_matrices
Statistical method
deliver the local treatment effect. The two most common approaches to estimation using an RDD are non-parametric and parametric (normally polynomial regression)
Regression discontinuity design
Regression_discontinuity_design
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
coefficient of variation in normally distributed data is often based on McKay's chi-square approximation for the coefficient of variation. Liu (2012) reviews methods
Coefficient_of_variation
Method of estimating the parameters of a statistical model
the quantity one wants to estimate. MAP estimation is therefore a regularization of maximum likelihood estimation. Assume that we want to estimate an unobserved
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Mathematical decision rule
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value
Bayes_estimator
Metric for fit of statistical models
Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. In
Goodness_of_fit
Statistical theorem
arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. The Rao–Blackwell
Rao–Blackwell_theorem
Function related to statistics and probability theory
becomes a function solely of the model parameters. In maximum likelihood estimation, the model parameter(s) or argument that maximizes the likelihood function
Likelihood_function
Generalization of the one-dimensional normal distribution to higher dimensions
JSTOR 2318494. Wyatt, John (November 26, 2008). "Linear least mean-squared error estimation" (PDF). Lecture notes course on applied probability. Archived from
Multivariate normal distribution
Multivariate_normal_distribution
Table that displays the frequency of variables
{\displaystyle \phi =\pm {\sqrt {\frac {\chi ^{2}}{N}}},} where χ2 is computed as in Pearson's chi-squared test, and N is the grand total of observations
Contingency_table
Lower bound on variance of an estimator
In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter. The result
Cramér–Rao_bound
Method of estimating a statistical model's parameters
In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a
Maximum_spacing_estimation
Model selection principle
extended to other forms of inductive inference and learning, for example to estimation and sequential prediction, without explicitly identifying a single model
Minimum_description_length
Statistical test
significance tests that are increasingly being used in situations where chi-squared tests were previously recommended. The general formula for test statistics
G-test
Statistical technique to aid interpretation of data
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to
Linear_trend_estimation
Family of statistical methods based on sampling of available data
coefficient. It has been called the plug-in principle, as it is the method of estimation of functionals of a population distribution by evaluating the same functionals
Resampling_(statistics)
Parameter estimation technique in statistics, particularly econometrics
conditions, and can therefore be thought of as a special case of minimum-distance estimation. The GMM estimators are known to be consistent, asymptotically
Generalized_method_of_moments
Statistical theorem
{\displaystyle -2\log(\Lambda )} asymptotically approaches the chi-squared ( χ 2 {\displaystyle \chi ^{2}} ) distribution under the null hypothesis H 0 {\displaystyle
Wilks'_theorem
Estimate of an unobservable underlying probability density function
In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable
Density_estimation
Kth smallest value in a statistical sample
Garg, Vikram V.; Tenorio, Luis; Willcox, Karen (2017). "Minimum local distance density estimation". Communications in Statistics - Theory and Methods. 46
Order_statistic
Statistical model validation technique
Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how
Cross-validation_(statistics)
Class of statistical estimators
objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators
M-estimator
Method of statistical inference
be equal given "conventional wisdom". 1900: Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively
Statistical_hypothesis_test
Sequence of data points over time
cannot adequately represent. Estimation of TVAR models typically involves methods such as kernel smoothing, recursive least squares, or Kalman filtering. Non-linear
Time_series
Statistical test
{\displaystyle Q>\chi _{1-\alpha ,h}^{2}} where χ 1 − α , h 2 {\displaystyle \chi _{1-\alpha ,h}^{2}} is the (1 − α)-quantile of the chi-squared distribution
Ljung–Box_test
Statistical considerations on how many observations to make
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample
Sample_size_determination
Method for model fitting in statistics
reduced chi-squared χ ν 2 {\displaystyle \chi _{\nu }^{2}} : M β = χ ν 2 ( X T W X ) − 1 , χ ν 2 = S / ν , {\displaystyle {\begin{aligned}M^{\beta }&=\chi _{\nu
Weighted_least_squares
Statistics concept
_{i=1}^{n}r_{i}^{2}\sim \chi _{n-1}^{2}.} This difference between n and n − 1 degrees of freedom results in Bessel's correction for the estimation of sample variance
Errors_and_residuals
Probabilistic problem-solving algorithm
Moral, G. Rigal, and G. Salut. "Estimation and nonlinear optimal control: Particle resolution in filtering and estimation: Experimental results". Convention
Monte_Carlo_method
Statistical test of variance
refers to an overall or a global test. Other names include F-test or Chi-squared test. It is a statistical test implemented on an overall hypothesis that
Omnibus_test
Statistical method for resampling
a form of resampling. It is especially useful for bias and variance estimation. The jackknife pre-dates other common resampling methods such as the bootstrap
Jackknife_resampling
Quality measure of a statistical method
are always minimum variance unbiased estimators. However the converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased
Efficiency_(statistics)
Single measure of some attribute of a sample
statistics, such as t-statistic, chi-squared statistic, f statistic Order statistics, including sample maximum and minimum Sample moments and functions thereof
Statistic
Kind of numerical parameter of a parametric family of probability distributions
linear estimators also exist, such as the L-moments. Maximum likelihood estimation can also be used. The following continuous probability distributions have
Shape_parameter
Type of scatter plot
ratio and its y value can be -log10 of the p value from a Chi-square test or a Chi-square test statistic. Volcano plots show a characteristic upwards
Volcano_plot_(statistics)
Mathematical concept
of p for which the sum of squares of deviations of calculated probabilities from measured frequencies (chi squared) is minimum. The generalization enhances
Probability distribution fitting
Probability_distribution_fitting
Data visualization
on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles. Minimum (Q0 or 0th percentile): the lowest
Box_plot
Statistics method
this provides an intuitive justification for this type of approach to estimation. Generalized estimating equations Method of moments (statistics) Generalized
Estimating_equations
Statistics concept
of view of estimation, since the regression function is linear in terms of the unknown parameters β0, β1, .... Therefore, for least squares analysis, the
Polynomial_regression
Probability distribution
distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two
Gamma_distribution
Concept in inferential statistics
table, or in some other way. Mathematics portal A/B testing, ABX test Estimation statistics Fisher's method for combining independent tests of significance
Statistical_significance
Probability distribution
scaled-inverse-chi-squared distribution with parameters ν {\displaystyle \nu } and τ 2 . {\displaystyle \ \tau ^{2}~.} The scaled-inverse-chi-squared distribution
Student's_t-distribution
Time series model
Chi-square table value, we reject the null hypothesis and conclude there is an ARCH effect in the ARMA model. If T'R² is smaller than the Chi-square table
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Statistical method
intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling
Bootstrapping_(statistics)
Simultaneous observation and analysis of more than one outcome variable
variables that summarise the original set. The underlying model assumes chi-squared dissimilarities among records (cases). Canonical (or "constrained") correspondence
Multivariate_statistics
Probability distribution
\beta )\,} . Chi-squared distribution: If X ∼ χ 2 ( α ) {\displaystyle X\sim \chi ^{2}(\alpha )\,} and Y ∼ χ 2 ( β ) {\displaystyle Y\sim \chi ^{2}(\beta
Beta_distribution
Statistical test used to test homoscedasticity
based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the number of
Bartlett's_test
Experimental designs for response surface methodology
reasonable (in fact, their designs kept in the range of 1.5 to 2.6). The estimation variance should more or less depend only on the distance from the centre
Box–Behnken_design
Probability distribution
distribution Log-normal distribution O'Hagan, A.; Leonard, Tom (1976). "Bayes estimation subject to uncertainty about parameter constraints". Biometrika. 63 (1):
Skew_normal_distribution
Nonparametric measure of rank correlation
)^{2}}}\leq \chi _{1,\alpha }^{2}\right\},} where χ 1 , α 2 {\displaystyle \chi _{1,\alpha }^{2}} is the α {\displaystyle \alpha } quantile of a chi-square distribution
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Family of probability distributions related to the normal distribution
exponential families includes the following: normal exponential gamma chi-squared beta Dirichlet Bernoulli categorical Poisson Wishart inverse Wishart
Exponential_family
Measure of covariance of components of a random vector
dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random
Covariance_matrix
Branch of statistics focusing on spatial data sets
random variable) theory to model the uncertainty associated with spatial estimation and simulation. A number of simpler interpolation methods/algorithms,
Geostatistics
Formal information theory restatement of Occam's Razor
Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection. It provides a formal information
Minimum_message_length
Statistical test that compares goodness of fit
approximations thereof: e.g. the Z-test, the F-test, the G-test, and Pearson's chi-squared test; for an illustration with the one-sample t-test, see below. If the
Likelihood-ratio_test
Statistical method for handling multiple comparisons
This idea was later developed into an algorithm and incorporated the estimation of m 0 {\displaystyle m_{0}} into procedures such as Bonferroni, Holm
False_discovery_rate
Type of numerical analysis
provides point estimates at observed values of x . {\displaystyle x.} Estimation of the complete dose-response curve without any additional assumptions
Isotonic_regression
involves the observation that Pearson's chi-squared test is an approximate test. Suppose Pearson's chi-squared test is used to ascertain whether a six-sided
Exact_test
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
Female
Japanese
Variant spelling of Japanese Chou, CHO means "butterfly."
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Male
English
French form of English Stewart, STUART means "house guard; steward." In use by the English and Scottish.
Female
Vietnamese
Vietnamese name CHI means "tree branch."
Surname or Lastname
English
English : patronymic from Squire.
Female
Thai/Siamese
Thai name NGAM-CHIT means "good heart."
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Boy/Male
Italian
Squire.
Surname or Lastname
English
English : variant spelling of Chinn.Chinese : variant of Jin 1.Chinese : Cantonese variant of Qian.Chinese : variant of Qin 1.Chinese : variant of Qin 2.Chinese : variant of Jin 2.Chinese : variant of Jin 3.Korean : there are four Chinese characters for the surname Chin, representing five clans. At least three of the clans have origins in China; most of them migrated to Korea during the Kory{ou} period (ad 918–1392).
Boy/Male
French Latin
A squire.
Female
Vietnamese
Vietnamese name THI means "poem."
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Surname or Lastname
English
English : variant of Squire.
Male
Scandinavian
 Variant spelling of Scandinavian Kai, possibly CAI means "lord." Compare with another form of Cai.
Male
Welsh
 Welsh name, possibly derived from Latin Caius, CAI means "lord." In Arthurian legend, this was the name of a Knight of the Round Table. Compare with another form of Cai.
Boy/Male
African
God'.
Boy/Male
English American
Shieldbearer.
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Female
Japanese
(æµ) Japanese name CHIE means "wisdom."
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
Boy/Male
Muslim/Islamic
Leader pioneer
Girl/Female
Indian
Ice Forest
Boy/Male
Tamil
Iyyappan | இயà¯à®¯à®¾à®ªà¯à®ªà®¨
Lord Ayyappan, Youthful
Boy/Male
Indian, Punjabi, Sikh
Unique Love
Boy/Male
Tamil
Excellent
Boy/Male
Indian
Winner in the Earth
Female
English
Variant spelling of English Destiny, DESTINEE means "fate, fortune."
Girl/Female
Gujarati, Hindu, Indian
Sensitive
Girl/Female
British, English
Form of Dolores; Lady of Sorrows
Female
English
Anglicized form of Scottish Gaelic Ealasaid, AILSA means "God is my oath." The name was derived from Ailsa Craig, the name of an island off Scotland, also known by the Gaelic names Allasa Creag and Creag Ealasaid ("Elisabeth's Rock" or Elspeth's Rock"). The island is known by many other names, including Old Norse Alfsigesey, meaning "Alfsigr's Island."Â
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
MINIMUM CHI-SQUARE-ESTIMATION
n.
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
pl.
of Minimus
n.
A square; a measure; a rule.
a.
Even; leaving no balance; as, to make or leave the accounts square.
n.
A square. See 1st Squire.
n.
Having the toe square.
pl.
of Minimum
n.
The product of a number or quantity multiplied by itself; thus, 64 is the square of 8, for 8 / 8 = 64; the square of a + b is a2 + 2ab + b2.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
Hence, anything which is square, or nearly so
n.
To place at right angles with the keel; as, to square the yards.
a.
Having four equal sides and four right angles; as, a square figure.
imp. & p. p.
of Square
n.
To multiply by itself; as, to square a number or a quantity.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
n.
A square piece or fragment.
a.
Forming a right angle; as, a square corner.
n.
Minimum.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
a.
Rendering equal justice; exact; fair; honest, as square dealing.