Statistics — Page 37
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Reilly's Law of Retail Gravitation
Reilly's law of retail gravitation is a deterministic model that predicts how an intermediate town's retail trade divides between two larger competing cities. Formulated by William J. Reilly in 1931 by analogy with Newtonian gravity, it sta...
Relational Gompertz Fertility Model
The relational Gompertz model expresses any population's cumulative fertility schedule as a simple linear transformation of a fixed standard schedule, after both are mapped through a double-logarithm (gompit) transform. Developed by William...
Relative Index of Inequality
The relative index of inequality (RII) is the relative counterpart of the slope index of inequality: instead of the absolute difference in a health outcome between the bottom and top of the socioeconomic hierarchy, it expresses that differe...
Remote Sensing Classification
Remote sensing classification assigns discrete thematic labels — such as forest, urban, water, or cropland — to pixels in a satellite or aerial image based on their spectral, spatial, and temporal properties. It underpins land-use/land-cove...
Repeat Victimization Analysis
Repeat victimization analysis studies the sharply elevated short-term risk that the same target — a household, person, or business — is victimized again soon after an initial offense. Established as a crime-prevention priority by Ken Pease,...
Repeated-measures ANOVA
Repeated-measures ANOVA is a parametric hypothesis test that compares three or more measurements taken from the same individuals — typically across time points or conditions — to decide whether their means differ. It extends one-way ANOVA t...
Resource Curse Analysis
Resource curse analysis is the empirical study of the paradox that economies rich in natural resources — oil, gas, minerals — often grow more slowly, remain less democratic, and suffer more conflict than resource-poor economies. Jeffrey Sac...
Retirement Transition Event-History Analysis
Retirement transition event-history analysis applies survival and hazard modeling to the timing of the move out of the labor force in later life, treating retirement as a datable event whose risk unfolds over time. Rather than asking only w...
RevPAR Performance Analysis
RevPAR performance analysis is the practice of measuring, decomposing, and benchmarking hotel performance using revenue per available room and its companion metrics. RevPAR distills a hotel's success into a single figure, rooms revenue divi...
Ripley K Function
The Ripley K function, introduced by Brian Ripley in 1977, is a second-order summary statistic for spatial point patterns. It measures how the number of points within a given distance d of a typical point compares to what would be expected...
Risk Parity Portfolio
Risk parity is a portfolio weighting model, formalised by Maillard, Roncalli and Teïletche (2010), in which every asset contributes an equal share of the total portfolio risk. It needs only the covariance (risk) structure of the assets and...
Risk-Neutral Valuation
Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harri...
Robust ADF Unit Root Test
The Robust ADF unit root test extends the classical ADF procedure with improvements that correct for size distortions arising from heteroscedastic or serially correlated errors, and from poor lag-length selection. Drawing on GLS detrending...
Robust ANCOVA
Robust ANCOVA is a covariate-adjusted group comparison that replaces classical ANCOVA's ordinary least squares estimation with resistant methods — typically trimmed means or M-estimators — so that the test retains valid Type I error control...
Robust ANOVA
Robust ANOVA compares the central tendency of three or more groups when the classical assumptions of normality and equal variances fail. It combines Welch's heteroscedasticity-adjusted statistic, introduced by Welch in 1951, with trimmed-me...
Robust AR model
The robust AR model fits an autoregressive time series specification using estimation methods — typically M-estimators or bounded-influence estimators — that resist distortion from outliers and heavy-tailed error distributions. Unlike OLS-b...
Robust ARCH model
The Robust ARCH model extends the classical Autoregressive Conditional Heteroscedasticity framework by replacing the standard maximum-likelihood estimator with robust alternatives that downweight or eliminate the influence of outliers. This...
Robust ARDL bounds test
The Robust ARDL bounds test is an augmented version of the Pesaran-Shin-Smith (2001) ARDL bounds testing approach that resolves its two key weaknesses: size distortion under mixed integration orders and the degenerate-case problem. It intro...
Robust ARIMA model
Robust ARIMA extends the classical ARIMA framework to detect and correct the influence of outliers and structural breaks during estimation. By jointly identifying anomalous observations and re-estimating model parameters, it produces coeffi...
Robust ARMA Model
The Robust ARMA model extends the classical Autoregressive Moving Average framework by replacing the sensitive least-squares loss with outlier-resistant estimation methods — typically M-estimators or median-based approaches. This protects c...
Robust Approximate Bayesian Computation
Robust ABC extends standard Approximate Bayesian Computation to handle outliers, model misspecification, and sensitivity to summary statistic choice. By replacing conventional distance measures with robust alternatives — such as composite s...
Robust Arellano-Bond GMM
The Robust Arellano-Bond GMM estimator applies the Arellano-Bond first-difference GMM approach to dynamic panel data while computing heteroscedasticity- and autocorrelation-consistent (robust) standard errors. This combination handles the N...
Robust Bayesian Inference
Robust Bayesian inference extends standard Bayesian analysis by replacing a single prior distribution with a class of plausible priors and examining how much the posterior conclusions change across that class. Instead of committing to one p...
Robust Bayesian Model Averaging
Robust Bayesian model averaging extends standard BMA by replacing sensitive conjugate priors with heavy-tailed or mixture priors (e.g., mixtures of g-priors), and optionally robust likelihoods, so that posterior model probabilities and aver...