Statistics — Page 39
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Robust GARCH model
The Robust GARCH model extends the classical GARCH framework to handle outliers and heavy-tailed innovations that commonly appear in financial return series. By down-weighting extreme observations through a robust innovation term, it produc...
Robust GLS
Robust GLS extends classical Generalized Least Squares by pairing GLS coefficient estimation with heteroscedasticity- and autocorrelation-consistent (HAC) standard errors, or by using M-estimation within the GLS framework. It corrects for n...
Robust Geary's C
Robust Geary's C adapts the classical Geary contiguity ratio — a measure of spatial autocorrelation based on pairwise squared differences between neighbouring locations — to resist distortion by spatial outliers and influential observations...
Robust Generalized linear model
A Robust Generalized Linear Model fits the standard GLM family — linear, logistic, Poisson, and others — using M-type estimating equations that down-weight outlying or influential observations. The result is coefficient estimates and standa...
Robust Getis-Ord Gi*
The Robust Getis-Ord Gi* statistic extends the classical Gi* hot-spot measure to handle outliers in spatial data. By using robust estimators of the mean and variance — such as trimmed means, medians, or down-weighted influential observation...
Robust Gibbs Sampling
Robust Gibbs sampling is a Markov chain Monte Carlo strategy that pairs the coordinate-wise Gibbs sampler with heavy-tailed or outlier-resistant model specifications — most commonly Student-t likelihoods — so that the posterior inference is...
Robust Granger Causality
Robust Granger causality extends the classic Granger causality framework by using bootstrap-based or heteroscedasticity-robust critical values rather than asymptotic chi-squared tables. This makes the test reliable in finite samples and whe...
Robust Hamiltonian Monte Carlo
Robust Hamiltonian Monte Carlo (Robust HMC) is a family of extensions to standard HMC designed to maintain geometric ergodicity and sampling efficiency when the posterior has heavy tails, strong curvature variation, or near-degenerate geome...
Robust Hausman Test
The Robust Hausman Test is a heteroscedasticity- and autocorrelation-robust version of the Hausman specification test, used to choose between fixed-effects and random-effects estimators in panel-data models. It builds on Hausman's 1978 test...
Robust Hierarchical Clustering
Robust hierarchical clustering extends classical agglomerative or divisive hierarchical clustering by replacing sensitive distance measures and linkage criteria with outlier-resistant alternatives, preserving cluster structure even when dat...
Robust Hierarchical Linear Model
Robust Hierarchical Linear Model (Robust HLM) extends standard HLM by replacing or protecting its standard errors against violations of distributional assumptions — chiefly non-normal residuals, heteroscedasticity, and influential clusters....
Robust Johansen Cointegration
The Robust Johansen Cointegration test extends the classical Johansen (1988, 1991) likelihood-ratio framework for determining the cointegrating rank of a multivariate I(1) system to settings where standard Gaussian assumptions fail — in par...
Robust K-means Clustering
Robust K-means clustering is an extension of classical k-means that protects cluster estimates from distortion caused by outliers or contaminated observations. By trimming a user-specified fraction of the most extreme points before updating...
Robust KPSS test
The Robust KPSS test is an extension of the classical Kwiatkowski-Phillips-Schmidt-Shin (1992) stationarity test that replaces the conventional long-run variance estimator with an outlier-robust or heteroscedasticity-robust counterpart, mai...
Robust Kalman Filter
The Robust Kalman Filter is an extension of the classical Kalman filter designed to maintain reliable state estimation when observations or process noise depart from the Gaussian assumption — particularly when data contain outliers, heavy-t...
Robust Kendall's tau
Robust Kendall's tau estimates the monotone association between two variables using rank-based concordance counts, but augments the standard procedure with outlier detection or Winsorization so that a small number of extreme observations ca...
Robust Kriging
Robust Kriging is a geostatistical interpolation method that extends classical kriging by replacing sensitive variogram estimation with outlier-resistant alternatives, most notably the Cressie-Hawkins robust estimator. It produces spatially...
Robust Kruskal-Wallis test
The robust Kruskal-Wallis test is a nonparametric, rank-based method for comparing three or more independent groups when data contain outliers, heavy tails, or heterogeneous spread. It augments the classical Kruskal-Wallis H statistic with...
Robust Latent Class Analysis
Robust latent class analysis (robust LCA) extends the standard latent class model by incorporating outlier-resistant estimation techniques — such as trimmed likelihood, M-estimation, or downweighting — so that atypical response patterns do...
Robust Latent Profile Analysis
Robust latent profile analysis identifies latent subgroups of individuals based on their continuous multivariate indicators while protecting parameter estimates from distortion by outliers or atypical observations. It extends standard laten...
Robust Local Indicators of Spatial Association
Robust Local Indicators of Spatial Association extend Anselin's LISA framework to handle outliers, extreme values, and spatially heterogeneous populations. By applying outlier-resistant adjustments to the spatial weights or the standardised...
Robust Logistic Regression
Robust Logistic Regression is a variant of logistic regression that is resistant to outliers and leverage points, fitting a binary or categorical outcome with Mallows-type weighted estimation. The robust framework for generalized linear mod...
Robust MA model
The Robust MA model applies robust estimation — typically M-estimation or bounded-influence methods — to the Moving Average time series model. By replacing the ordinary least squares loss with a bounded loss function, it produces parameter...
Robust MANOVA
Robust MANOVA is a multivariate analysis of variance procedure designed to remain valid when classical assumptions — multivariate normality and homogeneity of covariance matrices — are violated. It replaces raw means and standard covariance...