Statistics — Page 22
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Interactive Fixed Effects
Interactive Fixed Effects (IFE) extends standard fixed-effects panel models by allowing unit-specific intercepts to vary not just at the individual level but also with unobserved common time-varying factors. Introduced by Bai (2009), it mod...
Interest Rate Models
Interest rate models are structural models that describe how interest rates evolve over time within a stochastic differential equation framework. The family covers Vasicek's normal short-rate process (1977), the CIR square-root process, the...
Intergenerational Elasticity
The intergenerational elasticity of income (IGE) is the workhorse measure of economic mobility: the regression coefficient from regressing a child's adult log income on the parent's log income. It expresses the percentage by which a child's...
Interrater Reliability
Interrater reliability quantifies the degree to which two or more independent raters produce consistent scores when evaluating the same individuals or products. The family encompasses Cohen's kappa, introduced in 1960 for categorical judgme...
Intervening Opportunities Model
The intervening opportunities model, introduced by Samuel Stouffer in 1940, explains the volume of migration between two places not by the physical distance separating them but by the number of opportunities available at the destination rel...
Intraclass Correlation Coefficient
The Intraclass Correlation Coefficient (ICC) is a parametric reliability statistic that quantifies the degree of agreement or consistency among repeated measurements or multiple raters on a continuous outcome. The modern six-form taxonomy w...
Inverse Distance Weighting
Inverse distance weighting is a simple, deterministic method for estimating values at unsampled locations by taking a weighted average of nearby measured points, where closer points carry more weight. Introduced by Donald Shepard in 1968, i...
Jackknife
The jackknife is a classical resampling method that estimates the bias and variance of a statistic by systematically recomputing it with one observation left out at a time. Introduced by Quenouille in 1956 and later reviewed by Miller in 19...
Jackknife Estimation
Jackknife estimation is a classical resampling technique that computes the bias and variance of a statistical estimator by systematically leaving out one observation at a time and re-computing the statistic on each reduced sample. Introduce...
Johansen Cointegration Test
The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the...
Joint Model for Longitudinal and Survival Data
The joint model for longitudinal and time-to-event data, formalised by Tsiatis and Davidian in 2004 and extended comprehensively by Rizopoulos in 2012, simultaneously estimates a mixed-effects model for repeatedly measured biomarkers and a...
Jonckheere-Terpstra Test
The Jonckheere-Terpstra test is a nonparametric hypothesis test that detects a monotone trend across k ordered groups — testing whether the outcome rises (or falls) systematically as the group order increases. Developed independently by T....
Jump-Diffusion Model
The Merton Jump-Diffusion model, introduced by Robert C. Merton in 1976, extends Geometric Brownian Motion by adding sudden price jumps generated by a Poisson process. It captures the volatility smile and the fat-tailed return behaviour tha...
KPSS Test
The KPSS test, introduced by Kwiatkowski, Phillips, Schmidt and Shin in 1992, tests the null hypothesis that a series is stationary against the alternative that it contains a unit root — the reverse of the ADF and Phillips-Perron tests. By...
Kalman Filter
The Kalman filter is an optimal recursive algorithm for estimating the hidden state of a linear dynamical system from noisy measurements. At each time step it alternates between a prediction step — projecting the state forward using the sys...
Kalman Filter (Finance)
The Kalman filter is a recursive algorithm that estimates financial models with time-varying parameters, hidden factors, and noisy observations inside a dynamic state-space framework. The structural time series treatment was set out by Harv...
Kalman Filter with Measurement Error
The Kalman filter with measurement error is a recursive Bayesian state-space algorithm that estimates the true hidden state of a dynamic system from noisy observations. It explicitly separates process noise (system dynamics uncertainty) fro...
Kalman Filter with Missing Data
The Kalman filter with missing data extends the classical Kalman filter to handle time series in which some observations are absent. When an observation is missing at time t the update step is skipped and the state estimate is carried forwa...
Kaplan-Meier
The Kaplan-Meier estimator, introduced by Kaplan and Meier in 1958, is a non-parametric method that estimates the survival curve — the probability of remaining event-free over time — from right-censored time-to-event data. The log-rank test...
Kaplan-Meier Estimator
The Kaplan-Meier estimator is a nonparametric method for estimating the survival function S(t) — the probability that an individual survives beyond time t — from data that include censored observations. Introduced by Edward L. Kaplan and Pa...
Kelly Criterion
The Kelly Criterion (1956) is a formula for optimal bet sizing that maximizes the long-run logarithmic growth of wealth. It specifies the optimal fraction of capital to risk on each trade based on win probability and payoff ratio. The crite...
Kendall Tau Correlation
Kendall Tau is a nonparametric rank correlation coefficient introduced by Maurice G. Kendall in 1938 to measure the strength and direction of a monotone association between two ordinal or continuous variables. It is particularly suited to s...
Kendall's tau
Kendall's tau is a nonparametric measure of the ordinal association between two variables. It quantifies how consistently the relative ordering of one variable matches the ordering of another across all observation pairs, making it robust t...
Kernel Density Estimation
Kernel Density Estimation is a nonparametric method that estimates a continuous probability density by placing a smooth kernel function over each observation, without assuming any parametric distribution. It traces back to Rosenblatt (1956)...