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Specialized form of regression analysis, in statistics
In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship
Robust_regression
Moving average and polynomial regression method for smoothing data
Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its
Local_regression
Statistical modeling technique
regression relative to ordinary least squares regression is that the quantile regression estimates are more robust against outliers in the response measurements
Quantile_regression
Set of statistical processes for estimating the relationships among variables
called regressors, predictors, covariates, explanatory variables or features). The most common form of regression analysis is linear regression, in which
Regression_analysis
Type of statistics
significant advance in their applicability. Robust confidence intervals Robust regression Unit-weighted regression Sarkar, Palash (2014-05-01). "On some connections
Robust_statistics
Statistical modeling method
regression; a model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression
Linear_regression
1987 statistics book by Rousseeuw and Leroy
Robust Regression and Outlier Detection is a book on robust statistics, particularly focusing on the breakdown point of methods for robust regression
Robust Regression and Outlier Detection
Robust_Regression_and_Outlier_Detection
Method for solving certain optimization problems
maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers
Iteratively reweighted least squares
Iteratively_reweighted_least_squares
Statistical method for fitting a line
Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane (a form of simple linear regression) by choosing the median of the
Theil–Sen_estimator
Statistical optimality criterion
Median absolute deviation Ordinary least squares Robust regression "Least Absolute Deviation Regression". The Concise Encyclopedia of Statistics. Springer
Least_absolute_deviations
Topics referred to by the same term
Look up regression, regressions, or régression in Wiktionary, the free dictionary. Regression or regressions may refer to: Regression (film), a 2015 horror
Regression
Loss function used in robust regression
In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A
Huber_loss
In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator
Repeated_median_regression
by the presence of outliers . It is one of a number of methods for robust regression. Instead of the standard least squares method, which minimises the
Least_trimmed_squares
Information-theoretic measure
cross-entropy loss for logistic regression is equal to the gradient of the squared-error loss for linear regression (up to a constant factor). To see
Cross-entropy
Regression analysis
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination
Nonlinear_regression
Regularization technique for ill-posed problems
Ridge regression (also known as Tikhonov regularization, named for Andrey Tikhonov) is a method of estimating the coefficients of multiple-regression models
Ridge_regression
Belgian statistician (born 1956)
Minimum Covariance Determinant methods for robust scatter matrices. This work led to his book Robust Regression and Outlier Detection with Annick Leroy.
Peter_Rousseeuw
Statistical model for a binary dependent variable
combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) estimates the parameters of a logistic model
Logistic_regression
Asymptotic variances under heteroskedasticity
context of linear regression and time series analysis. These are also known as heteroskedasticity-robust standard errors (or simply robust standard errors)
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Four data sets with the same descriptive statistics, yet very different distributions
but should have a different regression line (a robust regression would have been called for). The calculated regression is offset by the one outlier
Anscombe's_quartet
Linear regression model with a single explanatory variable
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample
Simple_linear_regression
Class of statistical estimators
mixtures of distributions for regression. By the late 19th century, Smith (1888) introduced what is now recognized as the first robust M-estimator, already resembling
M-estimator
Statistics concept
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable
Polynomial_regression
Bayesian statistics textbook by Richard McElreath
and illustrating additional statistical models (smoothing splines, robust regression, and models not within the generalized linear mixed model framework)
Statistical_Rethinking
Method for estimating the unknown parameters in a linear regression model
especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is consistent
Ordinary_least_squares
Class of statistical models
(GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the
Generalized_linear_model
Observation far apart from others in statistics and data science
Extreme value theory Influential observation Random sample consensus Robust regression Spiders Georg Studentized residual Winsorizing Grubbs, F. E. (February
Outlier
Belgian mathematical statistician
research on topics in robust statistics including medoid-based clustering,[a] regression depth,[b] the medcouple for robustly measuring skewness,[c]
Mia_Hubert
Statistical method
squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression; instead of
Partial least squares regression
Partial_least_squares_regression
Statistical model for count data
Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes
Poisson_regression
Collection of data
provided online by UCLA Advanced Research Computing. Robust statistics – Data sets used in Robust Regression and Outlier Detection (Rousseeuw and Leroy, 1968)
Data_set
Medical statistical method
Passing–Bablok regression is a method from robust statistics for nonparametric regression analysis suitable for method comparison studies introduced by
Passing–Bablok_regression
{\theta }}))} . P. Rousseeuw and V. Yohai, Robust Regression by Means of S-estimators, from the book: Robust and nonlinear time series analysis, pages
S-estimator
Topics referred to by the same term
median regression, an algorithm for robust linear regression This disambiguation page lists articles associated with the title Median regression. If an
Median_regression
Type of statistical model
can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became
Multilevel_model
weighted non-linear least squares, and ordinary least squares with generated regressors. To fix ideas, let { W i } i = 1 n ⊆ R d {\displaystyle \{W_{i}\}_{i=1}^{n}\subseteq
Two-step_M-estimator
Measure of linear correlation
Standardized covariance Standardized slope of the regression line Geometric mean of the two regression slopes Square root of the ratio of two variances
Pearson correlation coefficient
Pearson_correlation_coefficient
Regression for more than two discrete outcomes
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than
Multinomial logistic regression
Multinomial_logistic_regression
Family of functions to transform data
heavy-tailed so that the assumption of normality is not realistic and a robust regression approach leads to a more precise model. Economists often characterize
Power_transform
Type of numerical analysis
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations
Isotonic_regression
linear regression (known as linear discriminant analysis in the classification case). Unit-weighted regression is a method of robust regression that proceeds
Unit-weighted_regression
Method for model fitting in statistics
(WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance
Weighted_least_squares
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
Statistical method of dividing data into equal-sized intervals for analysis
related is the subject of least absolute deviations, a method of regression that is more robust to outliers than is least squares, in which the sum of the absolute
Quantile
Overview of and topical guide to regression analysis
outline is provided as an overview of and topical guide to regression analysis: Regression analysis – use of statistical techniques for learning about
Outline of regression analysis
Outline_of_regression_analysis
Regression diagnostic Regression dilution Regression discontinuity design Regression estimation Regression fallacy Regression-kriging Regression model validation
List_of_statistics_articles
Theorem related to ordinary least squares
of the Regression Model". Econometric Theory. Oxford: Blackwell. pp. 17–36. ISBN 0-631-17837-6. Goldberger, Arthur (1991). "Classical Regression". A Course
Gauss–Markov_theorem
Transformation of statistics by limiting extreme values
DescTools::Winsorize(a, probs = c(0.05, 0.95)) Trimmed estimator Huber loss Robust regression Lee, Brian K.; Lessler, Justin; Stuart, Elizabeth A. (2011). "Weight
Winsorizing
Method for estimating demand or value
hedonic regression traces its roots to Court (1939), which was an analysis of automobile prices and automobile features. Hedonic regression is presently
Hedonic_regression
Statistics concept
distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead
Errors_and_residuals
American statistician (1937–2023)
with Hodges and Lehmann and for the Theil–Sen estimator, a form of robust regression that fits a line to two-dimensional sample points by choosing the
Pranab_K._Sen
Least squares approximation of linear functions to data
^{\mathsf {T}}\mathbf {y} .} Optimal instruments regression is an extension of classical IV regression to the situation where E[εi | zi] = 0. Total least
Linear_least_squares
Regression analysis for modeling ordinal data
In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e.
Ordinal_regression
Statistical hypothesis test
the linear regression to the result from the t-test. From the t-test, the difference between the group means is 6-2=4. From the regression, the slope
Student's_t-test
American statistician
visualization,[A] equivalences between binary regression and survival analysis,[B] and robust regression.[C] Gasko completed her Ph.D. in statistics at
Miriam_Gasko_Donoho
Model of enzyme kinetics
example Greco and Hakala, have claimed that non-linear regression is always superior to regression of the linear forms of the Michaelis–Menten equation
Michaelis–Menten_kinetics
Difference between a variable's observed value and a reference value
sensitive to outliers compared to the least squares method, making it a robust regression technique in the presence of skewed or heavy-tailed residual distributions
Deviation_(statistics)
Process in software development
list (link) Miyazaki, Y. Terakado, M. Ozaki, K. Nozaki, H. (1994). "Robust regression for developing software estimation models". Journal of Systems and
Software development effort estimation
Software_development_effort_estimation
Middle quantile of a data set or probability distribution
multivariate distributions. The Theil–Sen estimator is a method for robust linear regression based on finding medians of slopes. The median filter is an important
Median
Regression model for ordinal dependent variables
logit model or proportional odds logistic regression is an ordinal regression model—that is, a regression model for ordinal dependent variables—first
Ordered_logit
Family of continuous probability distributions
McDonald, J.; Michefelder, R.; Theodossiou, P. (2009). "Evaluation of Robust Regression Estimation Methods and Intercept Bias: A Capital Asset Pricing Model
Skewed generalized t distribution
Skewed_generalized_t_distribution
Statistical regression technique
multilevel regression with poststratification model involves the following pair of steps: MRP step 1 (multilevel regression): The multilevel regression model
Multilevel regression with poststratification
Multilevel_regression_with_poststratification
Statistical method
parametric (normally polynomial regression). The most common non-parametric method used in the RDD context is a local linear regression. This is of the form: Y
Regression discontinuity design
Regression_discontinuity_design
Method of spatial measurement using laser
reflective intensity data is also used for curb detection by making use of robust regression to deal with occlusions. Road marking is detected using a modified
Lidar
Dutch econometrician (1924–2000)
econometrics. He is also responsible for the Theil–Sen estimator for robust regression. Theil's archives are kept at Hope College. Theil published a series
Henri_Theil
Statistical property
which performs an auxiliary regression of the squared residuals on the independent variables. From this auxiliary regression, the explained sum of squares
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Class of statistical survival models
itself be described as a regression model. There is a relationship between proportional hazards models and Poisson regression models which is sometimes
Proportional_hazards_model
Concept in statistical mathematics
Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable
Segmented_regression
Statistical regression where the dependent variable can take only two values
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word
Probit_model
Type of compact allowing trade unions to edit US federal project contracts
they employed robust regression methods to account for variances in school construction materials/techniques and location. Robust regression is a statistical
Project_Labor_Agreement
Machine learning algorithm
continuous values (typically real numbers) are called regression trees. More generally, the concept of regression tree can be extended to any kind of object equipped
Decision_tree_learning
Approximation method in statistics
as the least angle regression algorithm. One of the prime differences between Lasso and ridge regression is that in ridge regression, as the penalty is
Least_squares
Statistical technique
used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the
Principal component regression
Principal_component_regression
Approximation method in statistics
the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box–Cox transformed regressors ( m ( x ,
Non-linear_least_squares
Statistical technique
taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models
Total_least_squares
Integrated set of tools
determine what problems changes in the code may have introduced. Having a robust regression test suite is especially critical in areas where there are short release
Parasoft_C/C++test
Statistical methods to improve the quality of manufactured goods
Taguchi methods (Japanese: タグチメソッド) are statistical methods, sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured
Taguchi_methods
Sequence of data points over time
simple function (also called regression). The main difference between regression and interpolation is that polynomial regression gives a single polynomial
Time_series
Branch of statistics
the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function
Mathematical_statistics
Collection of statistical models
notation in place, we now have the exact connection with linear regression. We simply regress response y k {\displaystyle y_{k}} against the vector X k {\displaystyle
Analysis_of_variance
Type of statistical measure over subsets of a dataset
various applications in image signal processing. In a moving average regression model, a variable of interest is assumed to be a weighted moving average
Moving_average
Continuous probability distribution on the unit interval
; Ovaskainen, Otso; Dunson, David B. (18 May 2026). "Scalable and robust regression models for continuous proportional data". Journal of the American
Continuous binomial distribution
Continuous_binomial_distribution
Statistical linear model
model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is
General_linear_model
Concept in regression analysis mathematics
least-angle regression algorithm. An important difference between lasso regression and Tikhonov regularization is that lasso regression forces more entries
Regularized_least_squares
Regression models accounting for possible errors in independent variables
error model is a regression model that accounts for measurement errors in the independent variables. In contrast, standard regression models assume that
Errors-in-variables_model
Method of data analysis
principal components and then run the regression against them, a method called principal component regression. Dimensionality reduction may also be appropriate
Principal_component_analysis
American systems biologist and bioengineer (born 1965)
engineering gene networks using singular value decomposition and robust regression". Proc Natl Acad Sci U S A. 99 (9): 6163–8. Bibcode:2002PNAS...99
James_J._Collins
Experimental design that is optimal with respect to some statistical criterion
criterion results in minimizing the average variance of the estimates of the regression coefficients. C-optimality This criterion minimizes the variance of a
Optimal_experimental_design
Statistical model
including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a
Fixed_effects_model
Indicator for how well data points fit a line or curve
remaining 51% of the variability is still unaccounted for. For regression models, the regression sum of squares, also called the explained sum of squares,
Coefficient_of_determination
Method used in statistics, pattern recognition, and other fields
categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain
Linear_discriminant_analysis
Statistical method
linear regression models. This simple case reveals a substantial amount about the estimator. These include its relationship to ridge regression and best
Lasso_(statistics)
Statistics concept
regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression,
Regression_validation
Probability distribution
; Dahl, B. K.; Ovaskainen, O.; Dunson, D. B. (2026). Scalable and robust regression models for continuous proportional data. Journal of the American Statistical
Continuous Bernoulli distribution
Continuous_Bernoulli_distribution
Statistical measure of the magnitude of a phenomenon
sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, and the risk of a particular event
Effect_size
Method of statistical analysis
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables
Bayesian_linear_regression
Parametric model in survival analysis
term is incorporated in the survival model, the regression parameter estimates from AFT models are robust to omitted covariates, unlike proportional hazards
Accelerated failure time model
Accelerated_failure_time_model
Range to estimate an unknown parameter
under Excel Confidence interval calculators for R-Squares, Regression Coefficients, and Regression Intercepts Weisstein, Eric W. "Confidence Interval". MathWorld
Confidence_interval
Regression algorithm
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron
Least-angle_regression
ROBUST REGRESSION
ROBUST REGRESSION
Surname or Lastname
English
English : variant spelling of Rout.
Male
Dutch
, supplanter.
Surname or Lastname
English
English : variant spelling of Roebuck.
Surname or Lastname
English
English : patronymic from the personal name Robb.
Boy/Male
Muslim
Strong, Tough, Robust
Surname or Lastname
English, French, German, Dutch, Hungarian (Róbert), etc
English, French, German, Dutch, Hungarian (Róbert), etc : from a Germanic personal name composed of the elements hrÅd
‘renown’ + berht ‘bright’, ‘famous’. This is found occasionally
in England before the Conquest, but in the main it was introduced into
England by the Normans and quickly became popular among all classes of
society. The surname is also occasionally borne by Jews, as an
Americanized form of one or more like-sounding Jewish surnames.A Robert from La Rochelle, France is documented in Trois-Rivières,
Quebec, in 1666, with the secondary surname
Male
Dutch
, supplanter.
Boy/Male
Indian
Strong, Tough, Robust
Biblical
strong; robust
Male
Czechoslovakian
, bright fame.
Boy/Male
Arabic, Muslim
Strong; Tough; Robust; Forceful
Surname or Lastname
English and French
English and French : variant of Robert.
Boy/Male
German American Shakespearean Teutonic English French Scottish
Famed, bright; shining. An all-time favorite boys' name since the Middle Ages. Famous Bearers:...
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, Czechoslovakian, Danish, Dutch, English, Finnish, French, German, Indian, Irish, Italian, Jamaican, Netherlands, Polish, Scottish, Swedish, Swiss, Teutonic
Bright with Fame; Famed; Bright; Shining; An All-time Favorite Boys Name Since the Middle Ages; A; 14th-century King Robert the Bruce; Robert Burns the Poet
Boy/Male
Christian & English(British/American/Australian)
Robust
Surname or Lastname
English
English : nickname for a person with red hair, from Middle English, Old French rous ‘red(-haired)’ (Latin russ(e)us).Americanized spelling of German Raus.
Male
English
 English form of Anglo-Saxon Hreodbeorht, ROBERT means "bright fame." Compare with another form of Robert.
Male
French
 Norman French form of Latin Robertus, ROBERT means "bright fame." Compare with another form of Robert.
Boy/Male
Hindu, Indian, Marathi
Strong; Robust
Boy/Male
Native American
Locust.
ROBUST REGRESSION
ROBUST REGRESSION
Girl/Female
Latin
A poetic name for Great Britain.
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Name of a River
Girl/Female
Muslim
Helper, Publisher, Diffuser, Spreader, Protector
Girl/Female
Hindu, Indian
The Atmosphere
Boy/Male
Hindu
Huge and gigantic, The mighty one
Boy/Male
Hindu, Indian, Marathi
Well Decorated
Boy/Male
Polish
Protective shield.
Female
English
English name derived from the vocabulary word, TAWNY means "light brown, tawny."
Girl/Female
Hindu, Indian
Atom God
Male
Portuguese
Portuguese form of Roman Latin Ovidius, OVÃDIO means "sheep herder."
ROBUST REGRESSION
ROBUST REGRESSION
ROBUST REGRESSION
ROBUST REGRESSION
ROBUST REGRESSION
n.
A composition used in making a rust joint. See Rust joint, below.
a.
Pithy; robust.
a.
Robust.
a.
Evincing strength; indicating vigorous health; strong; sinewy; muscular; vigorous; sound; as, a robust body; robust youth; robust health.
v. t.
To cook by surrounding with hot embers, ashes, sand, etc.; as, to roast a potato in ashes.
adv.
In a robust manner.
v. t.
To rouse; to disturb; as, to roust one out.
n.
The quality or state of being robust.
v. t.
To dry and parch by exposure to heat; as, to roast coffee; to roast chestnuts, or peanuts.
n.
The locust tree. See Locust Tree (definition, note, and phrases).
n.
See Herb Robert, under Herb.
v.
To wake from sleep or repose; as, to rouse one early or suddenly.
a.
Roasted; as, roast beef.
n.
See Roust.
a.
Sickly; not robust.
v. t.
To cause to contract rust; to corrode with rust; to affect with rust of any kind.
n.
Roast.
a.
Requiring strength or vigor; as, robust employment.
v. t.
See Roust, v. t.
v. t.
To mark or indicate by a rebus.