Statistics — Page 21
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Hierarchical Kalman Filter
The Hierarchical Kalman Filter (HKF) extends the classic Kalman filter to systems with multiple levels or scales of state representation. It applies Kalman recursions at each level of a hierarchy — from coarse to fine resolution or from glo...
Hierarchical Linear Model
The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-...
Hierarchical Linear Modeling
Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within...
Hierarchical Markov Chain Monte Carlo
Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertai...
Hierarchical Particle Filter
A hierarchical particle filter extends Sequential Monte Carlo to state-space models with multiple levels of latent variables. Particles are propagated at each level of the hierarchy, allowing the method to track both fine-grained state dyna...
Hierarchical Variational Inference
Hierarchical variational inference (HVI) extends standard variational inference by placing a richer, hierarchical structure on the variational family itself. Instead of using a simple mean-field approximation, HVI introduces auxiliary laten...
Historical Event-History Demography
Historical event-history demography applies the statistical machinery of survival and hazard analysis to longitudinal individual-level historical data, modelling the risk that a person experiences a demographic event—death, marriage, migrat...
Holm Correction
The Holm correction, introduced by Sture Holm in 1979, is a step-down multiple-comparison procedure that controls the family-wise error rate (FWER) at level α while rejecting at least as many hypotheses as the classical Bonferroni correctio...
Holt-Winters
Holt-Winters triple exponential smoothing is a forecasting model that extends Holt's double smoothing by adding a seasonal component, introduced by Peter Winters in 1960 building on Charles Holt's work. It tracks three evolving quantities —...
Hot Spot Analysis
Hot Spot Analysis uses the Getis-Ord Gi* local spatial statistic to identify geographic locations where high or low attribute values cluster together to a degree that is statistically significant. Each feature is evaluated in relation to it...
Hotelling's T² Test
Hotelling's T² test is a multivariate parametric hypothesis test that simultaneously compares the mean vectors of two independent groups across multiple continuous outcome variables. It was introduced by Harold Hotelling in 1931 as the dire...
Huber Regression
Huber regression is a robust linear regression method, introduced by Peter J. Huber in 1964, that resists the influence of outliers by treating small and large residuals differently. It applies a squared (OLS-like) loss to small residuals a...
Huff Model
Proposed by David Huff in 1964, the Huff Model is a probabilistic spatial interaction model that estimates the likelihood that consumers located in a given geographic zone will choose to shop at a particular retail outlet. It extends determ...
Hull-White Model
The Hull-White model (1990) is a one-factor short-rate model with time-dependent mean reversion and volatility, designed to fit the initial yield curve exactly. It generalizes the Vasicek model to allow better calibration to observed bond a...
Hurdle Model
The hurdle model is a two-part count-data model introduced by Mullahy (1986). A first stage models the binary choice of crossing a hurdle (a zero versus a non-zero count), and a second stage models the strictly positive counts with a zero-t...
Ideal Point Estimation
Ideal point estimation recovers the latent policy positions — ideal points — of political actors from their observed binary choices, most often legislators' yea/nay votes on roll calls. Building on the spatial theory of voting and formalize...
Ideological Constraint Analysis
Ideological constraint analysis measures the degree to which an individual's or a public's political attitudes hang together in a coherent, predictable structure, the extent to which knowing a person's position on one issue lets you predict...
Im-Pesaran-Shin Test
The Im-Pesaran-Shin (IPS) test, introduced by Im, Pesaran, and Shin in 2003, is a panel unit-root test designed for heterogeneous panels where the autoregressive coefficient is allowed to differ across cross-sectional units. It averages ind...
Immigrant Earnings Assimilation
Immigrant earnings assimilation analysis asks how the wages of the foreign-born evolve relative to comparable natives as immigrants spend more years in the host country. Barry Chiswick's 1978 study established the canonical approach: regres...
Impulse Response Function
The Impulse Response Function (IRF) traces the dynamic response of each variable in a Vector Autoregression (VAR) system to a one-unit shock in one of its error terms over a user-specified forecast horizon. It is the primary tool for struct...
Independent samples t-test
The independent samples t-test is a parametric hypothesis test that determines whether the means of two independent, unrelated groups differ significantly on a continuous outcome variable. Derived from Gosset's 1908 t-distribution, it is on...
Independent t-test
The independent samples t-test is a parametric hypothesis test that compares the means of two independent groups to decide whether they differ significantly. It builds on the t-distribution introduced by Student (W. S. Gosset) in 1908 and a...
Influence Diagnostics
Influence diagnostics are a family of post-fit measures that quantify how much each single observation affects a fitted regression. Cook's distance was introduced by R. Dennis Cook in 1977, with leverage and DFFITS formalised by Belsley, Ku...
Intention-to-Migrate Prediction
Intention-to-migrate prediction models stated plans to migrate as a forecast of actual migration behavior, taking seriously that what people say they will do is informative but imperfect. Migration surveys routinely ask whether respondents...