Statistics — Page 59
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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 Synthetic Control Method
The robust synthetic control method extends the classic synthetic control estimator by providing statistically valid uncertainty quantification and inference. Developed by Cattaneo, Feng and Titiunik (2021), it addresses a core limitation o...
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...
Robust Wilcoxon signed-rank test
The robust Wilcoxon signed-rank test extends the classical Wilcoxon signed-rank test by incorporating outlier-resistant location measures or robust preprocessing steps, improving inference on paired data when extreme observations or heavy-t...
Robust Zero-Inflated Model
The robust zero-inflated model extends standard zero-inflated count regression — which handles excess zeros via a mixture of a point mass at zero and a count distribution — by replacing or supplementing classical maximum likelihood with rob...
Robust Zivot-Andrews test
The Robust Zivot-Andrews test extends the classic Zivot-Andrews (1992) unit root test to provide reliable inference when the error term may be heteroscedastic or non-normal. It tests whether a time series has a unit root while endogenously...
Robust chi-square test
The robust chi-square test extends the classic Pearson chi-square framework to remain reliable when standard assumptions — especially the minimum expected-cell-count rule — are violated. Using power divergence statistics (Cressie & Read, 19...
Robust frequency analysis
Robust frequency analysis applies outlier-resistant estimation and resampling or exact methods to the counting and tabulation of categorical data, reducing the distortion caused by extreme observations, sparse cells, or violations of large-...
Robust independent samples t-test
The robust independent samples t-test compares the central tendency of two independent groups using trimmed means and Winsorized variances, making it substantially less sensitive to outliers and non-normality than the classical Student or W...
Robust one-sample t-test
The robust one-sample t-test replaces the ordinary mean with a trimmed mean and the sample variance with a Winsorized variance to compare a population location against a hypothesized value. It retains the t-test decision framework while sha...