Statistics — Page 34
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
M/M/1 Queue
The M/M/1 queue is the foundational single-server queueing model in which customers arrive according to a Poisson process with rate λ, are served one at a time by a single server with exponentially distributed service times at rate μ, and w...
M/M/c Queue
The M/M/c queue is a multi-server stochastic model in which customers arrive according to a Poisson process at rate λ, are served by c identical servers each with exponentially distributed service times at rate μ, and wait in a single commo...
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...
MCP Penalized Regression
MCP (Minimax Concave Penalty) is a variable selection method developed by Zhang (2010) that uses a concave penalty function for automated feature selection. Like SCAD, MCP addresses bias in lasso by avoiding shrinkage of large coefficients,...
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...
MRQAP Network Regression
Multiple regression quadratic assignment procedure (MRQAP) extends QAP to the regression setting: it predicts a dependent relational matrix from several independent relational matrices on the same actors — for example, modeling who collabor...
Machine Learning-Augmented Coarsened Exact Matching
Machine Learning-Augmented Coarsened Exact Matching extends Coarsened Exact Matching (Iacus, King & Porro, 2012) by using supervised machine learning to automate and optimise the coarsening step — the discretisation of continuous covariates...
Machine Learning-Augmented Counterfactual Impact Evaluation
Machine learning-augmented counterfactual impact evaluation combines the credibility of potential-outcomes causal inference with the flexibility of modern ML algorithms. Rather than imposing parametric functional forms for confounders, ML l...
Machine Learning-Augmented Entropy Balancing
Machine learning-augmented entropy balancing (ML-EB) combines Hainmueller's entropy balancing reweighting scheme with a machine-learning outcome model to produce a doubly-robust causal estimator. By jointly optimising covariate balance weig...
Machine Learning-Augmented Fuzzy Regression Discontinuity
ML-augmented fuzzy RDD extends the classical fuzzy regression discontinuity design by replacing parametric polynomial approximations with flexible machine learning estimators. Where standard fuzzy RDD uses IV-style estimation at a threshold...
Machine Learning-Augmented Interrupted Time Series
Machine Learning-Augmented Interrupted Time Series (ML-ITS) estimates the causal effect of a discrete intervention by training a machine learning model on pre-intervention time series data, projecting a counterfactual trajectory into the po...
Machine Learning-Augmented Inverse Probability Weighting
Machine learning-augmented inverse probability weighting replaces parametric logistic regression with flexible ML algorithms to estimate treatment propensity scores, then reweights the sample to balance treated and control units. By leverag...
Machine Learning-Augmented Marginal Structural Model
The machine learning-augmented marginal structural model combines the causal rigour of Robins et al.'s MSM framework with flexible, data-adaptive ML algorithms for estimating propensity scores and outcome models. By replacing parametric nui...