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Estimation method that minimizes the mean square error
signal processing, a minimum mean square error estimator (MMSE estimator) is an estimation method which minimizes the mean square error (MSE), which is a
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Measure of the error of an estimator
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures
Mean_squared_error
Unbiased statistical estimator minimizing variance
} A Bayesian analog is a Bayes estimator, particularly with minimum mean square error (MMSE). An efficient estimator need not exist, but if it does and
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Statistical measure
The root mean square deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and
Root_mean_square_deviation
Rule for calculating an estimate of a given quantity based on observed data
the "estimators". The attractiveness of different estimators can be judged by looking at their properties, such as unbiasedness, mean square error, consistency
Estimator
Statistical property
because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage
Bias_of_an_estimator
Statistical property
The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution
Standard_error
Approximation method in statistics
where the errors have a mean of zero, are uncorrelated, normally distributed, and have equal variances, the best linear unbiased estimator of the coefficients
Least_squares
Condition for optimality of Bayesian estimator
Bayesian estimator. Loosely stated, the orthogonality principle says that the error vector of the optimal estimator (in a mean square error sense) is
Orthogonality_principle
Method for estimating the unknown parameters in a linear regression model
unbiased estimators when the errors are homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimum-variance mean-unbiased
Ordinary_least_squares
Theorem related to ordinary least squares
restricting to unbiased estimators, minimum mean squared error implies minimum variance. The goal is therefore to show that such an estimator has a variance no
Gauss–Markov_theorem
Statistics concept
observable prediction errors: The mean squared error (MSE) refers to the amount by which the values predicted by an estimator differ from the quantities
Errors_and_residuals
Middle quantile of a data set or probability distribution
medians of the subsamples. Any mean-unbiased estimator minimizes the risk (expected loss) with respect to the squared-error loss function, as observed by
Median
Mathematical decision rule
\theta \,p(\theta |x)\,d\theta .} This is known as the minimum mean square error (MMSE) estimator. If there is no inherent reason to prefer one prior probability
Bayes_estimator
Statistical amount
al. (1988) when treating the weighted mean as a combination of a weighted total estimator divided by an estimator of the population size, based on the
Weighted_arithmetic_mean
Measure of variation in statistics
but it is still consistent. Its mean squared error, on the other hand, may be lower than that of the unbiased estimator. If the population of interest
Standard_deviation
Method of estimating the parameters of a statistical model, given observations
instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal
Maximum_likelihood_estimation
Statistical algorithm
finding the filter coefficients that relate to producing the least mean square of the error signal (difference between the desired and the actual signal).
Least_mean_squares_filter
Probability distribution
biased estimator σ ^ 2 {\displaystyle \textstyle {\hat {\sigma }}^{2}} is better than the s 2 {\textstyle s^{2}} in terms of the mean squared error (MSE)
Normal_distribution
Summary statistic of variability
accuracy is very closely related to the mean squared error (MSE) method which is just the average squared error of the forecasts. Although these methods
Average_absolute_deviation
Class of statistical estimators
statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum
M-estimator
Measure of linear correlation
\quad } therefore r is a biased estimator of ρ . {\displaystyle \rho .} The unique minimum variance unbiased estimator radj is given by where: r , n {\displaystyle
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical method for resampling
other than the mean. This simple example for the case of mean estimation is just to illustrate the construction of a jackknife estimator, while the real
Jackknife_resampling
Quality measure of a statistical method
calculated by finding the mean squared error. More formally, let T be an estimator for the parameter θ. The mean squared error of T is the value MSE ( T ) =
Efficiency_(statistics)
Branch of statistics
all unbiased estimators. Due to the bias-variance decomposition, they are optimal in the sense that they minimise the mean squared error among all unbiased
Parametric_statistics
Concept in statistics
(parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed
Kernel_density_estimation
Parameter estimation via sample statistics
unbiased estimators. According to the bias-variance decomposition, the variance of an unbiased estimator is equal to its mean squared error (MSE), which
Point_estimation
Statistical theorem
transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar
Rao–Blackwell_theorem
Indicator for how well data points fit a line or curve
the errors and the dependent variable instead of estimating them. Ingram Olkin and John W. Pratt derived the minimum-variance unbiased estimator for the
Coefficient_of_determination
Method for fitting a statistical model to data
empirical distribution. Often-used estimators such as ordinary least squares can be thought of as special cases of minimum-distance estimation. While consistent
Minimum-distance_estimation
Single measure of some attribute of a sample
sample mean is an unbiased estimator of the population mean. This means that the expected value of the sample mean equals the true population mean. A descriptive
Statistic
Type of statistics
based on the mean, are typically bounded above by the nominal size of the test. The same is not true of M-estimators and the type I error rate can be substantially
Robust_statistics
Regularization technique for ill-posed problems
ridge regression estimator (RR). This provides a more precise ridge parameters estimate, as its variance and mean square estimator are often smaller
Ridge_regression
Statistical measure of the magnitude of a phenomenon
education research. A similar effect size estimator for multiple comparisons (e.g., ANOVA) is the Ψ root-mean-square standardized effect: Ψ = 1 k − 1 ⋅ ∑ j
Effect_size
Statistical property
which assume that the modelling errors all have the same variance. While the ordinary least squares (OLS) estimator is still unbiased in the presence
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Algorithm that estimates unknowns from a series of measurements over time
the best possible linear estimator in the minimum mean-square-error sense, although there may be better nonlinear estimators. It is a common misconception
Kalman_filter
Statistical measure of how far values spread from their average
the population (see Mean squared error § Variance) and introduces bias. This always consists of scaling down the unbiased estimator (dividing by a number
Variance
Method for model fitting in statistics
{\boldsymbol {\beta }}}=X^{\textsf {T}}Wy} .} If the errors are correlated, the resulting estimator is the BLUE if the weight matrix is equal to the inverse
Weighted_least_squares
Probability distribution
\end{aligned}}} Other estimators also exist, such as Finney's UMVUE estimator, the "Approximately Minimum Mean Squared Error Estimator", the "Approximately
Log-normal_distribution
Statistical model to calculate the value of multiple quantities as they change over time
maximum likelihood estimator (MLE) of the covariance matrix differs from the ordinary least squares (OLS) estimator. MLE estimator:[citation needed] Σ
Vector_autoregression
Linear regression model with a single explanatory variable
that of the normality of the error terms, the estimator of the slope coefficient will itself be normally distributed with mean β and variance σ 2 / ∑ i (
Simple_linear_regression
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard deviation (RSD), is a standardized
Coefficient_of_variation
Study of collection and analysis of data
estimators, a widely used class of estimators. Root mean square error is simply the square root of mean squared error. Many statistical methods seek to
Statistics
Numeric quantity representing the center of a collection of numbers
Heronian mean Identric mean Lehmer mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root mean square (quadratic mean) Rényi's
Mean
Loss function used in robust regression
the mean-unbiased, minimum-variance estimator of the mean (using the quadratic loss function) and the robustness of the median-unbiased estimator (using
Huber_loss
Correction for sample variance bias
unbiased estimator of standard deviation. The corrected estimator often has a higher mean squared error (MSE) than the uncorrected estimator. Furthermore
Bessel's_correction
Statistical hypothesis test
by the continuous chi-squared distribution. This assumption is not quite correct and introduces some error. To reduce the error in approximation, Frank
Chi-squared_test
Branch of statistics to estimate models based on measured data
Maximum likelihood estimators Bayes estimators Method of moments estimators Cramér–Rao bound Least squares Minimum mean squared error (MMSE), also known
Estimation_theory
Mathematical relation assigning a probability event to a cost
{\theta }})^{2}\right].} An estimator found by minimizing the mean squared error estimates the posterior distribution's mean. In density estimation, the
Loss_function
Complete set of items that share at least one property in common
likely it is that the sample mean will be close to the population mean. Data collection system Horvitz–Thompson estimator Sample (statistics) Stratum (statistics)
Statistical_population
Probability distribution
the skewness and kurtosis estimators used in BMDP and in MINITAB (at that time) had smaller variance and mean-squared error in normal samples, but the
Beta_distribution
Least squares approximation of linear functions to data
{\boldsymbol {\beta }}}} is known, then a Bayes estimator can be used to minimize the mean squared error, E { ‖ β − β ^ ‖ 2 } {\displaystyle E\left\{\|{\boldsymbol
Linear_least_squares
Uniform distribution on an interval
sample mid-range, i.e. the arithmetic mean of the sample maximum and the sample minimum, which is the UMVU estimator of the midpoint (and also the maximum
Continuous uniform distribution
Continuous_uniform_distribution
Minimax estimator Minimisation (clinical trials) Minimum chi-square estimation Minimum distance estimation Minimum mean square error Minimum-variance
List_of_statistics_articles
Statistical modeling method
Bayes method Errors and residuals Lack-of-fit sum of squares Line fitting Linear classifier Linear equation Logistic regression M-estimator Multivariate
Linear_regression
Problem in statistical estimation
numbers: 19, 40, 42 and 60. A frequentist approach (using the minimum-variance unbiased estimator) predicts the total number of tanks produced will be: N ≈
German_tank_problem
Asymptotic variances under heteroskedasticity
the OLS point estimator remains unbiased, it is not "best" in the sense of having minimum mean square error, and the OLS variance estimator V ^ [ β ^ O
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Lower bound on variance of an estimator
unbiased estimator that achieves this bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all
Cramér–Rao_bound
Statistical method
estimators. Popular families of point-estimators include mean-unbiased minimum-variance estimators, median-unbiased estimators, Bayesian estimators (for
Bootstrapping_(statistics)
Phenomenon in statistics
population, as discussed at mean squared error: variance, but one can always do better (in terms of MSE) than the unbiased estimator; for the normal distribution
Shrinkage_(statistics)
Graphical representation of the distribution of numerical data
gives the minimum number of bins required for an asymptotically optimal histogram, where optimality is measured by the integrated mean squared error. The bound
Histogram
non-robust L-estimators include the minimum, maximum, mean, and mid-range. The trimmed equivalents are robust, however. Robust L-estimators used to measure
L-estimator
Family of statistical methods based on sampling of available data
of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence
Resampling_(statistics)
Method of estimating the parameters of a statistical model
posterior mean or median instead, together with credible intervals. This is both because these estimators are optimal under squared-error and linear-error loss
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Mathematical analysis technique
Next, the mean and variance of this PDF are needed, to characterize the derived quantity z. The mean and variance (actually, mean squared error, a distinction
Experimental uncertainty analysis
Experimental_uncertainty_analysis
Statistical technique
which the corresponding estimator β ^ L {\displaystyle {\widehat {\boldsymbol {\beta }}}_{L}} achieves the minimum prediction error is given by: L ( p −
Principal component regression
Principal_component_regression
Measure of statistical dispersion
75th percentile, so IQR = Q3 − Q1. The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset
Interquartile_range
Concepts from statistical hypothesis testing
Type I error, or a false positive, is the incorrect rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false
Type_I_and_type_II_errors
Theory in the field of statistics
heteroscedastic error variance in multiple linear regression. MINQUE estimators also provide an alternative to maximum likelihood estimators or restricted
MINQUE
Statistical measure of association
population quantity as Cramér's V but with typically much smaller mean squared error. The rationale for the correction is that under independence, E [
Cramér's_V
Robust and nonparametric estimator of a population's location parameter
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter. For populations that are symmetric
Hodges–Lehmann_estimator
Probability distribution
it equal to zero yields the maximum likelihood estimator of the θ parameter, which equals the sample mean x ¯ {\displaystyle {\bar {x}}} divided by the
Gamma_distribution
Process of using data analysis for predicting population data from sample data
frequentist developments of optimal inference (such as minimum-variance unbiased estimators, or uniformly most powerful testing) make use of loss functions
Statistical_inference
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 ) {\displaystyle
Probit_model
Estimate of an interval in which future observations will fall
unbiased estimate, while dividing by n yields the maximum likelihood estimator, and either might be used. One then uses the quantile function with these
Prediction_interval
Method of data analysis
from the mean Mean subtraction is an integral part of the solution towards finding a principal component basis that minimizes the mean square error of approximating
Principal_component_analysis
Specialized form of regression analysis, in statistics
trimmed squares (LTS) is a viable alternative and is currently (2007) the preferred choice of Rousseeuw and Ryan (1997, 2008). The Theil–Sen estimator has
Robust_regression
Statistical hypothesis test
uncorrelated). Let α ^ , β ^ = least-squares estimators , S E α ^ , S E β ^ = the standard errors of least-squares estimators . {\displaystyle {\begin{aligned}{\hat
Student's_t-test
Statistical estimator for ratio of means
The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made
Ratio_estimator
formalising the idea that an estimator should have certain intuitively appealing qualities. Strictly speaking, "invariant" would mean that the estimates themselves
Invariant_estimator
Correlation of a signal with a time-shifted copy of itself, as a function of shift
OLS estimators are no longer the Best Linear Unbiased Estimators (BLUE). While it does not bias the OLS coefficient estimates, the standard errors tend
Autocorrelation
Type of average of a collection of numbers
{x}})^{2}} . The sample mean is also the best single predictor because it has the lowest root mean squared error. If the arithmetic mean of a population of
Arithmetic_mean
Non-parametric statistic used to estimate the survival function
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime
Kaplan–Meier_estimator
Statistical phenomenon
In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where
Regression_toward_the_mean
Procedure to estimate standard deviation from a sample
the standard error of s is σ 1 − c 4 2 {\displaystyle \sigma {\sqrt {1-c_{4}^{2}}}} , while the standard error of the unbiased estimator is σ c 4 − 2
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Statistical model
data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression
Fixed_effects_model
Probability distribution
This estimator is found using maximum likelihood estimator and also the method of moments. This estimator is unbiased and uniformly with minimum variance
Binomial_distribution
Function of the observed sample results
H_{0}).} The error that a practising statistician would consider the more important to avoid (which is a subjective judgment) is called the error of the first
P-value
Statistical method
average is no longer an optimal estimator, since the error in X ¯ {\displaystyle {\overline {X}}} might actually exceed the error in the least noisy measurement
Inverse-variance_weighting
Organized raw data that has not been otherwise processed or transformed
Discretization of continuous features Logistic regression § Minimum chi-squared estimator for grouped data Newbold, P.; Carlson, W.; Thorne, B. (2009)
Grouped_data
Statistical measure of variability
is a more robust estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such
Median_absolute_deviation
Property of a model
y_{n})\}} . We make "as well as possible" precise by measuring the mean squared error between y {\displaystyle y} and f ^ ( x ; D ) {\displaystyle {\hat
Bias–variance_tradeoff
Statistical considerations on how many observations to make
the observations are independent, this estimator has a (scaled) binomial distribution (and is also the sample mean of data from a Bernoulli distribution)
Sample_size_determination
Statistical hypothesis test
variance), as a preliminary step to testing for mean effects, there is an increase in the experiment-wise Type I error rate. Most F-tests arise by considering
F-test
Kth smallest value in a statistical sample
polynomial L-estimator – linear combinations of order statistics Rank-size distribution Selection algorithm Sample maximum and minimum Quantile Percentile
Order_statistic
Type of kernel induced by artificial neural networks
result, using gradient descent to minimize least-square loss for neural networks yields the same mean estimator as ridgeless kernel regression with the NTK
Neural_tangent_kernel
Range to estimate an unknown parameter
Kiefer, J. (1977). "Conditional Confidence Statements and Confidence Estimators (with discussion)". Journal of the American Statistical Association. 72
Confidence_interval
Statistic quantifying the association between two events
maximize (as in Fisher's exact test). Another alternative estimator is the Mantel–Haenszel estimator.[citation needed] The following four contingency tables
Odds_ratio
Measure of the asymmetry of random variables
symmetric unbiased estimator of the third cumulant and k 2 = s 2 {\displaystyle k_{2}=s^{2}} is the symmetric unbiased estimator of the second cumulant
Skewness
Statistical test
{se} ({\widehat {\theta }})} is the standard error (SE) of the maximum likelihood estimate (MLE), the square root of the variance. There are several ways
Wald_test
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
Female
English
Pet form of Welsh Mared, MEGAN means "pearl."Â
Male
English
Anglicized form of Irish Gaelic Cian, KEAN means "ancient, distant."
Boy/Male
English American
Shieldbearer.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Error-less
Male
English
 English occupational surname transferred to forename use, from the Latin word decanus, DEAN means "dean; ecclesiastical supervisor."
Male
English
French form of English Stewart, STUART means "house guard; steward." In use by the English and Scottish.
Male
French
A derivative of Anglo-Norman French Jehan, JEAN means "God is gracious." Compare with feminine Jean.
Surname or Lastname
English
English : variant of Squire.
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.
Girl/Female
Hindu, Indian
Without Error
Female
English
Scottish form of French Jeanne, JEAN means "God is gracious." Compare with masculine Jean.
Male
English
Anglicized form of Irish Gaelic Seán, SEAN means "God is gracious."
Boy/Male
British, English
Spear-man
Surname or Lastname
English
English : patronymic from Squire.
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Male
English
Scottish surname transferred to forename use, from a place name possibly ERROL means "to wander."Â
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Anglo Saxon
Terror.
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
Boy/Male
Greek
God fearing.
Boy/Male
Tamil
Duraimani | தà¯à®°à¯ˆà®®à®¾à®¨à¯€
Boy/Male
Tamil
Conqueror, Name of Arjun
Boy/Male
Native American
High backed wolf.
Boy/Male
Hindu, Indian, Traditional
Lord Shiva
Girl/Female
Muslim
Closer, Nearer
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Friendly; Friend
Boy/Male
Hebrew American
Jehovah exists.
Girl/Female
British, English, Greek
Song
Surname or Lastname
English
English : variant of Hinckley.
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
MINIMUM MEAN-SQUARE-ERROR-ESTIMATOR
a.
Having a shape broad for the height, with rectilineal and angular rather than curving outlines; as, a man of a square frame.
a.
Having four equal sides and four right angles; as, a square figure.
n.
Minimum.
a.
Rendering equal justice; exact; fair; honest, as square dealing.
imp. & p. p.
of Square
superl.
Of poor quality; as, mean fare.
n.
Hence, anything which is square, or nearly so
n.
Having the toe square.
a.
Even; leaving no balance; as, to make or leave the accounts square.
pl.
of Minimus
a.
Forming a right angle; as, a square corner.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
A square piece or fragment.
n.
A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.
pl.
of Minimum
n.
A square; a measure; a rule.
n.
To multiply by itself; as, to square a number or a quantity.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
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.
n.
A square. See 1st Squire.