Statistics — Page 15
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
ERS Point-Optimal Test
The Elliott-Rothenberg-Stock (ERS) Point-Optimal test, introduced in their landmark 1996 Econometrica paper, is a near-efficient parametric procedure for testing whether a univariate time series contains a unit root. By first applying GLS d...
ETS Model
ETS is a comprehensive exponential smoothing framework that automatically selects additive or multiplicative combinations of the error (E), trend (T) and seasonal (S) components of a time series. Formalised as an innovations state space mod...
Ecosystem-Service Choice Experiment
A discrete choice experiment is a survey-based, stated-preference method for valuing changes in ecosystem services that have no market price. As set out by Hanley, Wright and Adamowicz in 1998, respondents are shown a series of choice sets,...
Educational Growth Curve Modeling
Educational growth curve modeling is a longitudinal multilevel technique for describing and explaining how individual students change over time on an outcome such as reading or mathematics achievement. Building on the hierarchical linear mo...
Educational Hierarchical Linear Modeling
Educational hierarchical linear modeling (HLM) is a multilevel regression framework for data in which students are nested within classrooms and classrooms within schools. Formalized for education by Raudenbush and Bryk, it lets the intercep...
Educational Production Function
The educational production function is the economist's framework for relating the inputs of schooling — class size, teacher quality, expenditure, family background — to an output, usually measured achievement. Borrowing the production-funct...
Effect size analysis
Effect size analysis quantifies the practical magnitude of a statistical result independently of sample size. Rather than asking only whether a difference or relationship is statistically significant, it asks how large it is, using standard...
Elastic Net Regression
Elastic net regression combines the L1 (lasso) and L2 (ridge) penalties into a single regularized regression framework. Controlled by a mixing parameter alpha and a shrinkage strength lambda, it can simultaneously select variables and handl...
Emax Model
The Emax model is a nonlinear pharmacodynamic model that describes the relationship between drug concentration and biological effect. Introduced by Holford and Sheiner in 1981, it characterizes dose-response curves using three fundamental p...
Empirical Bayes
Empirical Bayes (EB) is an estimation strategy, introduced by Herbert Robbins in 1956 and developed into practical shrinkage estimators by Bradley Efron and Carl Morris in 1973, in which the hyperparameters of the prior distribution are est...
Engle-Granger Cointegration Test
The Engle-Granger two-step method tests whether two or more non-stationary I(1) time series share a common stochastic trend — that is, whether a linear combination of them is stationary. If cointegration is confirmed, an error-correction mo...
Environmental Kuznets Curve Estimation
Environmental Kuznets curve (EKC) estimation tests the hypothesis that environmental degradation first rises and then falls as a country grows richer, tracing an inverted-U relationship between per-capita income and pollution. The empirical...
Epigenetic Clock (DNA Methylation Age)
An epigenetic clock is a statistical predictor that estimates age from patterns of DNA methylation, the chemical marks on the genome that change in a regular way over the life course. The most influential is Steve Horvath's 2013 multi-tissu...
Equivalence Test (TOST)
The equivalence test using the Two One-Sided Tests (TOST) procedure is a parametric hypothesis test designed to demonstrate that the difference between two group means falls within a pre-specified equivalence region ±Δ. Introduced by Schuir...
Ethnic Enclave Effect Estimation
Ethnic enclave effect estimation measures the economic consequences of working within a co-ethnic enclave economy — a spatially concentrated cluster of immigrant-owned firms employing co-ethnic workers — rather than in the open secondary la...
Event History Turnover Analysis
Event history turnover analysis models not just whether employees leave but when they leave, treating tenure as a duration and the act of quitting as an event whose timing carries information. Paul Allison's 1984 monograph brought event his...
Event Study
The event study is a financial research method that measures the impact of a news release, policy change, or corporate event on asset prices through cumulative abnormal returns. Reviewed by MacKinlay (1997) and formalised econometrically by...
Expectation Propagation
Expectation Propagation (EP) is a deterministic message-passing algorithm for approximate posterior inference in Bayesian models, introduced by Thomas P. Minka at UAI 2001. It iteratively refines a set of local approximate factors — each dr...
Exploratory Structural Equation Modeling
Exploratory Structural Equation Modeling (ESEM) is a hybrid approach that combines exploratory factor analysis (EFA) with confirmatory factor analysis (CFA) and path modeling, developed by Asparouhov and Muthén (2009). ESEM relaxes restrict...
Exponential Smoothing
Exponential smoothing is a family of basic time-series forecasting models in which each new observation updates a smoothed estimate by a weighting parameter. Simple exponential smoothing (SES), introduced by Robert G. Brown in 1959, forecas...
Exposome-Wide Association Study
An exposome-wide association study (ExWAS), originally introduced as the Environment-Wide Association Study, applies the logic of the genome-wide association study to the environment. Where a GWAS scans hundreds of thousands of genetic vari...
Extreme Value Theory
Extreme Value Theory is a statistical framework for modelling the rare events that live in the tail of a probability distribution. As developed in Coles (2001) and applied to risk by McNeil, Frey & Embrechts (2005), it offers two standard r...
FAVAR
FAVAR is a multivariate time-series model that first compresses information from a very large set of variables into a few common factors, then includes those factors alongside the observed variables in a vector autoregression. It was introd...
FEVD
Forecast Error Variance Decomposition (FEVD) is a multivariate time series technique used within Vector Autoregression (VAR) frameworks to quantify what proportion of the forecast error variance of each variable is attributable to shocks fr...