Statistics — Page 25
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Long-Memory Models
Long-memory models are fractional-integration methods that capture genuine long memory through a hyperbolically decaying autocorrelation structure. ARFIMA, introduced by Granger and Joyeux (1980), models long memory in return series, while...
Longitudinal CFA
Longitudinal confirmatory factor analysis (longitudinal CFA) applies a theoretically specified measurement model to data collected at two or more time points. Its primary purpose is to verify that a scale measures the same latent construct...
Longitudinal Cronbach's Alpha
Longitudinal Cronbach's alpha assesses the internal consistency reliability of a scale at each wave of a repeated-measures study and examines whether that reliability remains stable across time. It is an essential step in longitudinal scale...
Longitudinal EFA
Longitudinal EFA applies exploratory factor analysis separately at each measurement occasion — or jointly across occasions — to discover whether the same latent factor structure emerges over time and whether factor loadings remain stable ac...
Loss Distribution Model
A Loss Distribution Model is a parametric statistical framework used in actuarial science to characterise the probabilistic behaviour of insurance claim amounts and frequencies. Developed comprehensively by Klugman, Panjer, and Willmot in t...
Lumsdaine-Papell Test
The Lumsdaine-Papell test, introduced by Robin Lumsdaine and David Papell in 1997, extends the Zivot-Andrews single-break unit-root test to allow for two simultaneous structural breaks in the intercept and/or linear trend of a time series....
M-Estimator
M-estimators are a robust generalisation of maximum likelihood estimation, formalised in the work of Peter J. Huber (Huber & Ronchetti, 2009). Instead of squaring every residual, they apply a bounded loss function so that large residuals fr...
MAD Estimation
Median Absolute Deviation estimation is a robust measure of statistical dispersion that replaces the standard deviation when outliers are present. Rooted in the influence-curve framework formalised by Hampel (1974), it summarises the spread...
MAIHDA
MAIHDA — Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy — is a quantitative method for studying intersectional inequalities. Introduced for intersectionality by Clare Evans and S. V. Subramanian in 2018, buildin...
MANCOVA
MANCOVA (Multivariate Analysis of Covariance) is a parametric hypothesis test that simultaneously compares two or more groups on multiple continuous dependent variables while statistically controlling for one or more covariates. It extends...
MANOVA
MANOVA is a parametric hypothesis test that simultaneously compares group means across multiple continuous dependent variables, controlling the inflation of Type I error that would result from running separate ANOVAs. Key multivariate test...
MCMC
Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analyt...
MCMC for Model Comparison
MCMC for model comparison uses Markov chain Monte Carlo algorithms to estimate the marginal likelihoods and Bayes factors needed to formally compare competing statistical models. Techniques such as reversible-jump MCMC and bridge sampling a...
MCMC with Measurement Error
MCMC with measurement error applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for the fact that covariates or outcomes are observed with error. By treating the true, unobserved values as latent variables a...
MCMC with missing data
MCMC with missing data is a Bayesian computational strategy that treats unobserved values as additional unknown parameters. By alternating between sampling the missing values from their predictive distribution and sampling the model paramet...
MGWR
Multiscale Geographically Weighted Regression, introduced by Fotheringham, Yang and Kang in 2017, is a spatial regression model that lets each coefficient vary across space at its own spatial scale. It generalises Geographically Weighted Re...
MIDAS Regression
MIDAS (Mixed Data Sampling) Regression is an econometric framework that directly incorporates high-frequency predictors into models for lower-frequency outcome variables without requiring temporal aggregation of the regressors. Introduced b...
MM-Estimator
The MM-estimator is a robust linear regression method introduced by Victor J. Yohai in 1987. It combines the high breakdown point of an S-estimator with the high efficiency of an M-estimator, so it resists outliers strongly while still usin...
Maki Cointegration Test
The Maki cointegration test extends cointegration testing to allow for an unknown number of endogenously-determined structural breaks in the cointegrating relationship. Introduced by Maki (2012), it builds on Gregory and Hansen (1996), enab...
Mann-Whitney U test
The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test, comparing two independent groups by ranking all observations together rather than relying on their means. It was introduced by H. B. Mann and D. R....
Marginal Structural Model
A marginal structural model is a causal modeling framework designed to estimate the effect of a time-varying treatment in the presence of time-varying confounders that are themselves affected by prior treatment. By reweighting observations...
Market Entry Timing Hazard Analysis
Market entry timing hazard analysis models both whether and when a firm enters a new market or emerging industrial subfield, treating time-to-entry as a survival outcome. Will Mitchell's 1989 study of incumbents facing emerging subfields fr...
Market Microstructure Analysis
Market microstructure analysis studies how prices form from tick-level trade and quote data, examining order-book dynamics, the bid-ask spread, and price discovery. The modern econometric framework was set out by Hasbrouck (2007) and extend...
Markov-Switching Model
The Markov regime-switching model lets the parameters of a time series change probabilistically across hidden regimes governed by a Markov chain. Introduced by Hamilton (1989) and developed further by Kim and Nelson (1999), it automatically...