Statistics — Page 40
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Robust Mahalanobis Distance
Robust Mahalanobis Distance flags multivariate outliers by measuring how far each observation lies from the centre of the data using a robust covariance estimate. It builds on the robust-distance framework of Rousseeuw and Van Zomeren (1990...
Robust Mann-Whitney U test
The Robust Mann-Whitney U test is a nonparametric two-group comparison that combines the rank-based logic of the classic Mann-Whitney U test with modern robust techniques — such as outlier screening, trimmed means, or robust variance estima...
Robust Markov chain Monte Carlo
Robust MCMC combines Markov chain Monte Carlo sampling with robustness techniques to produce reliable posterior inference when data contain outliers, when the assumed model is misspecified, or when the target distribution has heavy tails th...
Robust Mediation Analysis
Robust mediation analysis estimates the indirect effect of an independent variable on an outcome through one or more mediators using estimators that resist the influence of outliers and non-normal error distributions. By combining robust re...
Robust Mixed Model
The robust mixed model is a linear mixed-effects model for panel and repeated-measures data that tolerates outliers and heavy-tailed errors. It replaces the usual likelihood with bounded-influence estimating equations, building on the robus...
Robust Mixture Modeling
Robust mixture modeling fits finite mixture models — probabilistic clustering methods that assume data arise from a blend of underlying subpopulations — using component distributions or estimation strategies designed to be insensitive to ou...
Robust Moderated Mediation
Robust moderated mediation tests whether the indirect effect of X on Y through a mediator M varies as a function of a moderator W, while using robust estimation (percentile or bias-corrected bootstrap, heteroscedasticity-consistent standard...
Robust Moderation Analysis
Robust moderation analysis tests whether the effect of a predictor on an outcome depends on the level of a moderator variable, using estimation methods that remain valid under non-normality, heteroscedasticity, or the presence of influentia...
Robust Monte Carlo Simulation
Robust Monte Carlo simulation extends standard Monte Carlo by explicitly accounting for uncertainty in input distributions, model structure, or parameter assumptions. Rather than assuming a single fixed probability distribution for each inp...
Robust Moran's I
Robust Moran's I is an outlier-resistant adaptation of the classic Moran's I spatial autocorrelation statistic. By replacing the standard mean-based standardization with resistant measures of center and spread, it detects genuine geographic...
Robust Multidimensional Scaling
Robust multidimensional scaling recovers a low-dimensional spatial map from a matrix of pairwise dissimilarities while resisting distortion caused by outlying or erroneous proximity values. By replacing squared-error loss with a robust loss...
Robust Multinomial Logistic Regression
Robust multinomial logistic regression extends the standard multinomial logit model to handle outliers, influential observations, and mild misspecification of the response distribution. It replaces the conventional maximum likelihood score...
Robust Multiple Correspondence Analysis
Robust Multiple Correspondence Analysis extends classical MCA to datasets containing outlying or atypical rows of categorical data. By downweighting influential observations before the singular value decomposition, it produces a low-dimensi...
Robust Multiple linear regression
Robust multiple linear regression estimates the linear relationship between a continuous outcome and several predictors while being resistant to outliers and violations of the normality assumption. Instead of minimising the sum of squared r...
Robust NARDL
Robust NARDL marries the asymmetric cointegration framework of Shin, Yu, and Greenwood-Nimmo (2014) with outlier-resistant estimation. It decomposes a regressor into positive and negative partial sums, tests for asymmetric long-run relation...
Robust Negative Binomial Regression
Robust Negative Binomial Regression models overdispersed count outcomes using the negative binomial distribution while protecting coefficient inference against misspecification of the variance function. It pairs maximum-likelihood estimatio...
Robust OLS
Robust OLS applies ordinary least squares to estimate coefficients and then replaces the classical standard errors with heteroscedasticity-consistent (HC) standard errors — commonly called White standard errors. This leaves the point estima...
Robust PCA
Robust Principal Component Analysis is a dimensionality-reduction method that extracts reliable components when the data are contaminated by outliers and noise. Introduced by Candès, Li, Ma and Wright (2011), and developed in the ROBPCA app...
Robust PP Unit Root Test
The Robust Phillips-Perron unit root test extends the classical PP test by applying corrections — such as heteroskedasticity-consistent covariance estimation or wild-bootstrap critical values — that maintain valid inference when the error v...
Robust Panel Data Analysis
Robust panel data analysis applies standard panel estimators — fixed effects, random effects, or pooled OLS — while replacing conventional standard errors with cluster-robust or heteroscedasticity-consistent (HC) variants. The point estimat...
Robust Particle Filter
The Robust Particle Filter is a sequential Monte Carlo method that tracks hidden states in nonlinear, non-Gaussian systems while remaining resistant to outliers and model misspecification. It replaces the standard Gaussian likelihood with a...
Robust Path Analysis
Robust path analysis applies robust estimation — such as sandwich standard errors or M-estimation — to path models that specify directed causal relationships among observed variables. It preserves valid inference about path coefficients and...
Robust Pearson correlation
The robust Pearson correlation is an outlier-resistant measure of linear association between two continuous variables. By applying Winsorizing, trimming, or percentage-bend transformations before computing the classic Pearson r, it retains...
Robust Poisson Regression
Robust Poisson regression fits a Poisson log-linear model to a binary outcome but replaces the model-based variance with the empirical sandwich estimator. This yields valid standard errors and risk ratios even though Poisson variance assump...