Statistics — Page 41
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Robust Probit Model
The Robust Probit Model estimates the probability of a binary outcome using the probit link function while protecting inference from misspecification of the error distribution or heteroscedasticity. Coefficients are obtained via maximum lik...
Robust Quantile Regression
Robust Quantile Regression estimates conditional quantiles of a response variable while simultaneously downweighting the influence of outliers. By combining the asymmetric loss function of standard quantile regression with bounded-influence...
Robust Quantile-on-Quantile Regression
Robust Quantile-on-Quantile Regression extends the QQ framework of Sim and Zhou (2015) by adding resistance to outliers and heavy-tailed distributions. It estimates how each quantile of one variable responds to each quantile of another, pro...
Robust ROC analysis
Robust ROC analysis evaluates the diagnostic accuracy of a continuous or ordinal biomarker in distinguishing between two groups (e.g., diseased vs. healthy) while protecting against the distorting effects of outliers, non-normality, or dist...
Robust Random Effects Model
The Robust Random Effects model estimates panel data relationships using the GLS random effects estimator while replacing the conventional standard errors with sandwich (heteroscedasticity- and cluster-robust) variance estimates. This prote...
Robust Regression
Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust meth...
Robust Regression Discontinuity Design
Robust RDD extends the classical regression discontinuity design with bias correction and robust confidence intervals, addressing the under-coverage problem of conventional RDD inference. Developed by Calonico, Cattaneo, and Titiunik (2014)...
Robust Ridge regression
Robust Ridge regression combines M-estimation with L2 (ridge) regularization to produce coefficient estimates that are simultaneously resistant to outliers and stable under multicollinearity. It minimizes a robust loss function (such as Hub...
Robust SARIMA model
Robust SARIMA extends the classical Seasonal ARIMA framework by replacing the standard least-squares criterion with a robust loss function — such as an M-estimator — so that outliers and heavy-tailed innovations in seasonal time series cann...
Robust SVAR model
The Robust SVAR model extends the classical Structural VAR framework by incorporating robust estimation and inference methods that remain valid in the presence of heteroscedasticity, non-Gaussian errors, or outliers. By combining structural...
Robust Sequential Monte Carlo
Robust Sequential Monte Carlo (Robust SMC) extends standard particle filtering to handle outliers, heavy-tailed noise, and model misspecification in sequential data. By replacing Gaussian likelihood assumptions with heavier-tailed distribut...
Robust Simple linear regression
Robust simple linear regression fits a straight line through bivariate data using loss functions or weighting schemes that down-weight outliers, producing slope and intercept estimates that are far less sensitive to extreme observations tha...
Robust Spatial Autocorrelation
Robust spatial autocorrelation methods measure the degree to which nearby geographic units share similar values, while explicitly controlling for the distorting influence of spatial outliers and extreme observations. They extend classical s...
Robust Spearman Correlation
Robust Spearman correlation is an outlier-resistant measure of monotonic association between two variables. It applies robustification strategies — such as Winsorizing extreme ranks or using the percentage-bend approach — to protect Spearma...
Robust Structural Equation Modeling
Robust structural equation modeling (Robust SEM) applies the full SEM framework — simultaneous estimation of measurement and structural relations among latent variables — while using corrected test statistics and sandwich standard errors th...
Robust System GMM
Robust System GMM is a two-step panel data estimator that combines the difference and levels moment conditions of Blundell and Bond (1998) with Windmeijer's (2005) finite-sample correction to the two-step variance, producing valid inference...
Robust TGARCH
Robust TGARCH extends the Threshold GARCH model by replacing the conventional maximum likelihood objective with an estimator that is resistant to heavy-tailed innovations and outlying observations. It captures asymmetric volatility response...
Robust Test-Retest Reliability
Robust test-retest reliability quantifies how consistently a measure ranks or scores the same individuals across two occasions while protecting the estimate from distortion by outliers and non-normal score distributions. It replaces or supp...
Robust Time Series Analysis
Robust Time Series Analysis fits autoregressive, moving-average, and ARIMA models to series that contain outliers or structural breaks, using M-estimation or MM-estimation instead of ordinary least squares so that a few anomalous observatio...
Robust Universal Kriging
Robust Universal Kriging (RUK) is a geostatistical interpolation method that combines a spatially varying deterministic trend with a stochastic residual surface, while using robust estimators to protect the variogram and trend coefficients...
Robust VAR model
The Robust VAR model extends the classical Vector Autoregression framework by replacing ordinary least squares estimation with robust estimators — such as M-estimators or median-based methods — to reduce the influence of outliers, structura...
Robust VECM
Robust VECM extends the classical Vector Error Correction Model by replacing ordinary least squares estimation with outlier-resistant procedures — such as M-estimators, S-estimators, or least trimmed squares — so that cointegration relation...
Robust Variational Inference
Robust variational inference (RVI) extends standard variational inference by replacing the Kullback-Leibler divergence with a divergence measure that is less sensitive to outliers and model misspecification — such as the beta-divergence or...
Robust WLS
Robust WLS combines weighted least squares — which corrects for known or estimated heteroscedasticity — with robust M-estimation that down-weights influential outliers. The result is a regression estimator that is simultaneously efficient u...