Statistics — Page 48
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
TVP-VAR
TVP-VAR is a Bayesian multivariate time-series model in which both the VAR coefficients and the shock covariance matrix are allowed to evolve continuously over time as random walks. Introduced by Primiceri (2005) to study U.S. monetary poli...
Tail Risk Measures
Tail risk measures quantify the loss distribution beyond Value-at-Risk (VaR). Expected Shortfall — the expected loss given that VaR is exceeded — is the leading coherent risk measure, formalised by Artzner, Delbaen, Eber and Heath (1999) an...
Tau Estimator
The Tau estimator is a robust linear regression method introduced by Yohai and Zamar in 1988 that fits the model by minimising an efficient τ-scale of the residuals. It builds on the scale estimate of the S-estimator to combine a high break...
Technology Acceptance Model
The Technology Acceptance Model (TAM) is a theoretical model of why people accept or reject information technology, introduced by Fred Davis in 1989. Adapting the Theory of Reasoned Action, it posits that two beliefs—perceived usefulness an...
Test-Retest Reliability
Test-retest reliability quantifies the temporal consistency of a measure by correlating scores obtained from the same participants on two separate occasions. It is a cornerstone of psychometric validation, directly indicating whether a scal...
Theil-Sen Estimator
The Theil-Sen estimator is a robust linear regression method that estimates the slope as the median of the slopes computed over all pairs of data points. Introduced by Henri Theil in 1950 and extended by P. K. Sen in 1968, it tolerates outl...
Therapeutic Drug Monitoring
Therapeutic Drug Monitoring (TDM) is a clinical pharmacokinetic practice in which drug concentrations are measured in a patient's blood to guide individualized dosing. It applies principally to drugs with narrow therapeutic windows—where th...
Theta Method
The Theta Method is a univariate time-series forecasting model introduced by Assimakopoulos and Nikolopoulos in 2000. It decomposes a series into two theta lines that capture its long-run trend and its short-run dynamics, forecasts each lin...
Three-Stage Least Squares
Three-Stage Least Squares is a system estimator for simultaneous-equation models that accounts for the correlation of error terms across equations. Introduced by Zellner and Theil in 1962, it combines two-stage least squares with the seemin...
Threshold Panel VAR
The Threshold Panel VAR extends the standard vector autoregression framework to accommodate regime-switching behavior where relationships change when a threshold variable crosses a critical level. Introduced by Hansen (1996) and applied to...
Threshold Regression
Threshold regression is a nonlinear, regime-switching model in which the regression parameters take different values above and below an estimated threshold value of a threshold variable. The sample-splitting and threshold-estimation framewo...
Threshold and Smooth-Transition VAR
Threshold VAR and Smooth-Transition VAR are nonlinear multivariate time-series models in which the coefficients of a vector autoregression switch between regimes according to a threshold variable. Building on Tsay's 1998 treatment of multiv...
Thurstone Scaling
Thurstone Scaling, formally the Law of Comparative Judgment, is a psychometric model introduced by Louis Leon Thurstone in 1927 for deriving interval-level scale values from pairwise comparison data. By assuming that each stimulus evokes a...
Time Series Kalman Filter
The time series Kalman filter applies the Kalman filtering and smoothing algorithm within a state-space representation of time series models. It recursively extracts unobserved components — trend, seasonality, cycles, and irregular noise —...
Time series Bayesian hierarchical model
A time series Bayesian hierarchical model combines the hierarchical (multilevel) Bayesian framework with a dynamic state-space structure to analyse temporal data collected on multiple units or groups. Priors encode beliefs about both within...
Time series Bayesian inference
Time series Bayesian inference applies Bayes' theorem sequentially to time-ordered observations, maintaining a full probability distribution over hidden states and model parameters at every time step. This framework unifies state-space mode...
Time series Bayesian model averaging
Time series Bayesian model averaging (TS-BMA) combines forecasts from an ensemble of time series models — such as AR, VAR, or state-space specifications — by weighting each model by its posterior probability given observed data. Rather than...
Time series MCMC
Time series MCMC applies Markov chain Monte Carlo methods to Bayesian inference over time-ordered data. Rather than optimising a single parameter estimate, it draws samples from the full joint posterior of parameters and latent states, yiel...
Time series approximate Bayesian computation
Time series ABC is a likelihood-free Bayesian inference method that estimates the posterior distribution of model parameters for dynamical or time-indexed systems by comparing summary statistics of simulated trajectories to those of the obs...
Time series particle filter
The time series particle filter is a Sequential Monte Carlo method that tracks the hidden state of a nonlinear, non-Gaussian state-space model as new observations arrive one at a time. It represents the evolving posterior distribution over...
Time series sequential Monte Carlo
Time series sequential Monte Carlo (SMC), commonly called the particle filter, is a Bayesian simulation method that tracks the hidden state of a dynamical system as observations arrive one at a time. A cloud of weighted random samples — par...
Time series variational inference
Time series variational inference applies variational Bayes to sequential data, approximating the intractable posterior over latent states and parameters with a tractable family of distributions. By maximising the evidence lower bound (ELBO...
Time-Dependent Cox Regression
Time-dependent Cox regression is an extension of the standard Cox proportional hazards model, introduced through the counting-process formulation developed by Therneau and Grambsch (2000), that allows one or more predictor variables to take...
Time-varying Parameter Panel Data Analysis
Time-varying parameter (TVP) panel data analysis extends standard panel regression by allowing the slope coefficients to evolve over time for each unit. Instead of assuming a single fixed or random coefficient, the model lets each unit's re...