Statistics — Page 56
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Robust Fixed Effects Model
The robust fixed effects model combines the within-group estimator for panel data with variance-covariance matrices that remain valid under heteroscedasticity and within-unit error correlation. Introduced by Arellano (1987), cluster-robust...
Robust Friedman test
The robust Friedman test is a nonparametric procedure for comparing three or more related (within-subjects) conditions that replaces standard ranking or mean-based summaries with robust location estimates — typically trimmed means or Winsor...
Robust Fuzzy Regression Discontinuity
Robust Fuzzy Regression Discontinuity Design estimates a local average treatment effect (LATE) at a threshold where crossing the cutoff raises — but does not guarantee — treatment receipt. Introduced by Calonico, Cattaneo, and Titiunik (201...
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 Instrumental Variables
Robust Instrumental Variables estimation extends standard IV and two-stage least squares (2SLS) by guarding against weak-instrument bias and non-standard inference. Methods such as the Anderson-Rubin test, Limited Information Maximum Likeli...
Robust Interrupted Time Series
Robust Interrupted Time Series Analysis is a quasi-experimental method that estimates the causal effect of a policy or intervention on an aggregate outcome over time, using segmented regression fitted with outlier-resistant or heteroskedast...
Robust Inverse Probability Weighting
Robust Inverse Probability Weighting is a causal inference estimator that reweights observed units by stabilized or trimmed propensity score weights, then applies sandwich or bootstrap variance estimation to guard against model misspecifica...
Robust Item Analysis
Robust item analysis applies outlier-resistant statistical methods to the evaluation of individual test or scale items. Instead of classical means and Pearson correlations — both sensitive to extreme scores — it uses trimmed means, Winsoriz...
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...