Statistics — Page 30
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
KLM-GOMS
The Keystroke-Level Model (KLM), part of the Goals-Operators-Methods-Selection rules (GOMS) framework, is a computational method for predicting how long a user will take to accomplish a routine task using an interactive system. Developed by...
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...
Kano Model
The Kano Model is a framework for categorizing product or service features based on their impact on customer satisfaction. Developed by Noriaki Kano, this model distinguishes three types of features: basic (must-have) features that satisfy...
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)...
Kernel PCA
Kernel Principal Component Analysis (Kernel PCA) is a nonlinear dimensionality-reduction method introduced by Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller in 1997–1998. It extends classical linear PCA to curved, non-linear d...
Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov (KS) test is a nonparametric goodness-of-fit test that assesses whether a sample comes from a specified theoretical distribution, such as the normal or exponential. First formalised by Andrey Kolmogorov in 1933 and fu...
Kriging
Kriging is a geostatistical method that predicts the value of a continuous variable at unmeasured locations from nearby measurements, using the spatial correlation structure captured by a variogram. Formalised by Georges Matheron in 1963, i...
Kruskal-Wallis test
The Kruskal-Wallis H test is a nonparametric hypothesis test that compares three or more independent groups to decide whether their distributions (typically their medians) differ. Introduced by William Kruskal and W. Allen Wallis in 1952, i...
Kónya Bootstrap Causality
Introduced by László Kónya in 2006, this method tests Granger causality in heterogeneous panels by estimating a Seemingly Unrelated Regressions (SUR) system and deriving country-specific critical values through bootstrapping. Unlike pooled...
LCA
Latent class analysis is a probabilistic model-based clustering technique that identifies unobserved subgroups — latent classes — within a population on the basis of patterns of categorical, binary, or ordinal indicator responses. Originati...
LGC Model
The latent growth curve model is a structural equation modelling approach introduced by Meredith and Tisak (1990) for analysing change over time. It treats each individual's starting point (intercept) and rate of change (slope) as latent va...
LISA
LISA, introduced by Luc Anselin in 1995, is a local statistic that computes spatial autocorrelation separately for every observation rather than for the map as a whole. It pinpoints where high or low values cluster and where spatial outlier...
LMDI Decomposition
Log-Mean Divisia Index (LMDI) Decomposition is a quantitative technique for attributing changes in an aggregate indicator — most commonly energy consumption or CO₂ emissions — to its underlying driving factors, such as activity level, struc...