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MetodStatistik1,836 AI och ML1,661 Beslutsvetenskap932 Forskningsmetoder1,354 Mätning1,745 Kausalitet & evidens532 Forskningspraktik118

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Explainable RoBERTa-based Classification

Explainable RoBERTa-based classification fine-tunes a RoBERTa transformer model on labeled text data and then applies post-hoc interpretability methods — such as SHAP, LIME, or attention analysis — to reveal which tokens or features drove each prediction. This bridges state-of-the-art NLP performance with human-underst

Explainable Vision Transformer

Explainable Vision Transformer combines the strong image-recognition performance of Vision Transformers (ViT) with attribution techniques — such as relevance propagation, attention rollout, or gradient-weighted attention — that highlight which image regions drive each prediction. The approach enables researchers and pr

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 restrictive zero-loading assumptions of traditional CFA, allowing all indicators to load

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, forecasts series with a stable level, while Holt's double exponential smoothing, introd

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 routes: the Generalized Extreme Value (GEV) distribution for block maxima and the

research statistics

Factor Analysis

Factor analysis is a statistical technique for identifying latent (unobserved) dimensions underlying observed variables, developed by Louis Leon Thurstone in the 1930s and formalized by Jöreskog (1969). Exploratory factor analysis (EFA) discovers unknown factor structure from data; confirmatory factor analysis (CFA) te

Factor Analysis for Scale Development

Exploratory factor analysis (EFA) is a statistical method for discovering the underlying dimensional structure of a set of items or variables. Pioneered by Louis Thurstone in the mid-20th century, EFA is widely used to develop and validate psychometric scales by identifying groups of items that correlate together, ther

Factor Risk Model

A factor risk model is a multi-factor framework that links asset returns to systematic risk factors such as the market, value, size, and momentum. The Fama-French three- and five-factor models (1993) and Ross's Arbitrage Pricing Theory (1976) decompose portfolio risk and detect alpha.

experimental design

Factorial A/B Test

A factorial A/B test is a controlled online experiment that simultaneously manipulates two or more independent factors, each at two or more levels, exposing different user groups to every combination of factor levels. Rooted in Fisher's factorial design and operationalised at scale by tech companies, it enables researc

experimental design

Factorial Experiment

A factorial experiment is an experimental design in which two or more independent variables (factors) are manipulated simultaneously, and every combination of their levels is tested. Introduced by Ronald Fisher in the 1920s–1930s, it is the standard approach whenever a researcher needs to detect not only the main effec

Fama-MacBeth Regression

The Fama-MacBeth procedure is a two-step regression methodology for analyzing cross-sectional relationships while controlling for time-series structure. Introduced by Fama and MacBeth (1973), it first estimates time-series parameters for each cross-sectional unit, then regresses outcomes on those parameters across the

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 introduced by Bernanke, Boivin and Eliasz in 2005 to study monetary policy using hundr

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 from every other variable in the system. It is widely used by econometricians, mac

Fine-Gray Competing Risks Model

The Fine-Gray model is a semiparametric regression method for survival data in which two or more mutually exclusive event types compete to occur first. Proposed by Fine and Gray in 1999, it models the subdistribution hazard of each event type directly, allowing covariates to be linked to the cumulative incidence functi

signal processing

FIR Filter Design

Finite Impulse Response (FIR) filters are digital filters with an impulse response that settles to zero in finite time, making them fundamentally stable and easy to analyze. Unlike their IIR counterparts, FIR filters are inherently stable, can have exactly linear phase response, and are widely used in applications from

First-Difference Estimator

The First-Difference (FD) estimator is a panel data method that eliminates unobserved, time-invariant individual heterogeneity by subtracting each unit's observation in period t-1 from its observation in period t. By operating on changes rather than levels, FD removes any fixed individual effect that would otherwise co

Fisher Panel Unit-Root Test

The Fisher-type (Maddala-Wu) panel unit-root test, introduced in 1999, combines individual-level ADF unit-root p-values using Fisher's chi-squared meta-analytic framework to produce a single panel-level test statistic. Unlike the Levin-Lin-Chu approach, it does not impose a common autoregressive parameter across cross-

Fisher's exact test

Fisher's exact test is a nonparametric exact-probability test of independence for small-sample contingency tables, introduced by R. A. Fisher in 1922. Rather than relying on a large-sample approximation, it computes the exact probability of the observed table directly from the hypergeometric distribution.

Fixed Effects Model

The fixed effects (FE) model is the workhorse estimator for panel data when unobserved unit-specific characteristics are suspected to correlate with the regressors. By absorbing each entity's time-invariant heterogeneity into a separate intercept, FE isolates the causal effect of within-unit variation and eliminates om

Fixed Effects Panel Model

The fixed effects panel model estimates relationships in panel data (many units observed over time) by exploiting only the within-unit variation, so that unobserved time-invariant heterogeneity is controlled away. It is the central within estimator developed in Baltagi's Econometric Analysis of Panel Data (2005), and t

Fleiss' Kappa

Fleiss' Kappa is a non-parametric statistic for measuring the degree of agreement among three or more raters who classify items into mutually exclusive nominal categories. Introduced by Joseph L. Fleiss in 1971 as a generalization of Cohen's Kappa beyond two raters, it corrects observed agreement for the level of agree

Fligner-Killeen Test

The Fligner-Killeen test is a rank-based test that checks whether several independent groups share the same variance (scale). Introduced by Fligner and Killeen in 1976, it does not require the data to be normally distributed, making it a robust nonparametric alternative to the Levene and Bartlett tests.

FMOLS Estimator

Fully Modified OLS, introduced by Phillips and Hansen (1990), estimates the long-run coefficients of a cointegrating relationship among I(1) variables. It applies a semi-parametric correction to ordinary least squares to remove the bias that endogeneity and serial correlation otherwise induce in cointegrated time serie

forensic science

Forensic Likelihood Ratio

The Forensic Likelihood Ratio (LR) is a Bayesian framework for quantifying the weight of forensic evidence relative to two competing propositions — typically the prosecution and defence hypotheses. Formally developed and systematised by Colin Aitken and Franco Taroni in their 2004 Wiley monograph, the LR expresses how

Fourier ADF unit root test

The Fourier ADF unit root test extends the standard Augmented Dickey-Fuller framework by incorporating low-frequency Fourier terms into the deterministic component. This allows the test to approximate smooth, gradual structural breaks in the level or trend of a time series without requiring prior knowledge of break num

Fourier AR Model

The Fourier AR model extends the standard autoregressive specification by adding trigonometric (sine and cosine) terms to the deterministic component. This allows the model to capture smooth, gradual shifts in the mean or trend of a time series without requiring the researcher to locate or count structural break points

Fourier ARCH Model

The Fourier ARCH model extends the classical ARCH framework by incorporating trigonometric (Fourier) terms into the conditional variance equation. This allows the model to capture smooth, gradual shifts in volatility dynamics over time without assuming abrupt structural breaks, making it well-suited for long financial

Fourier ARDL Bounds Test

The Fourier ARDL bounds test augments the Pesaran-Shin-Smith cointegration framework with trigonometric (Fourier) terms that capture gradual, smooth structural breaks in the data-generating process. It tests for a long-run level relationship between variables without requiring the researcher to specify the number, timi

Fourier Arellano-Bond GMM

Fourier Arellano-Bond GMM is a dynamic panel estimator that augments the classic Arellano-Bond first-differenced GMM framework with Fourier trigonometric terms to capture smooth, gradual structural breaks in the time dimension. It handles endogeneity through lagged-level instruments while remaining robust to unknown no

Fourier ARIMA model

The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or number of breaks in advance. It is widely used in applied macroeconometrics and fin

Fourier ARMA model

The Fourier ARMA model augments the classical Autoregressive Moving Average framework with low-frequency Fourier (sine and cosine) terms to capture smooth, gradual shifts in the mean or trend of a time series. Unlike dummy-variable approaches, it requires no prior knowledge of when structural change occurred, approxima

Fourier DCC-GARCH

The Fourier DCC-GARCH model extends Engle's Dynamic Conditional Correlation GARCH framework by embedding Fourier trigonometric terms in the conditional mean or variance equations. This allows the model to approximate smooth, gradual structural shifts in volatility dynamics and inter-asset correlations without requiring

Fourier Dynamic Panel Data Model

The Fourier dynamic panel data model extends standard dynamic panel specifications by incorporating low-frequency trigonometric (Fourier) terms to flexibly capture smooth, gradual structural breaks or time-varying patterns in the data, without requiring knowledge of the exact number or timing of breaks.

Fourier EGARCH

Fourier EGARCH extends Nelson's (1991) Exponential GARCH model by embedding Fourier trigonometric terms in the conditional variance equation to capture smooth, gradual shifts in the unconditional variance level over time. This allows the model to handle structural breaks in volatility without requiring prior knowledge

Fourier Engle-Granger cointegration

The Fourier Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure by embedding low-frequency trigonometric (Fourier) terms in the cointegrating regression. This accommodates an unknown number of smooth structural breaks in the deterministic components without specifying their dates, prod

Fourier Fixed Effects Model

The Fourier fixed effects model extends standard panel fixed effects regression by augmenting the specification with low-frequency Fourier (trigonometric) terms. These sine and cosine components approximate unknown, smooth structural shifts in the time trend without requiring the researcher to pre-specify break dates,

Fourier GARCH Model

The Fourier GARCH model embeds trigonometric Fourier terms into a standard GARCH framework to capture smooth, gradual shifts in the conditional variance process without requiring knowledge of exact structural break dates. By approximating unknown break patterns with sinusoidal functions, it jointly models volatility cl

Fourier GLS

Fourier GLS embeds low-frequency trigonometric (Fourier) terms into a generalized least squares framework to capture smooth, gradual structural change in a time series without requiring the researcher to specify when or how many breaks occurred. The approach is particularly valued in unit root testing and cointegration

Fourier Granger Causality

The Fourier Granger causality test extends the classic Granger causality framework by embedding low-frequency Fourier terms in the VAR equation, allowing the causal relationship to shift gradually over time without requiring the researcher to pre-specify the number or location of structural breaks.

Fourier Hausman test

The Fourier Hausman test extends the classical Hausman endogeneity test by augmenting the regression with Fourier trigonometric terms — sines and cosines of time — so that the test remains valid even when the data-generating process contains smooth structural breaks or gradual nonlinearities that conventional linear sp

Fourier Johansen cointegration

The Fourier Johansen cointegration test extends the classical Johansen trace and maximum-eigenvalue tests by embedding low-frequency Fourier terms in the deterministic component of the VECM. This allows the test to remain valid when cointegrating relationships experience gradual, smooth regime shifts that standard Joha

Fourier KPSS test

The Fourier KPSS test extends the standard KPSS stationarity test by embedding a flexible Fourier series in the deterministic component of the model. This approach captures smooth, gradual structural breaks in the level or trend of a time series without requiring the researcher to specify the number or timing of those

Fourier MA Model

The Fourier MA model combines a Moving Average (MA) error structure with Fourier series terms — sine and cosine pairs — to capture complex or high-frequency seasonal patterns in time series data. It is particularly useful when the seasonal period is long or irregular, making classical seasonal ARIMA parameterisation in

Fourier NARDL

Fourier NARDL extends the Nonlinear ARDL (NARDL) bounds-testing framework by adding Fourier trigonometric terms to the error-correction equation, allowing the model to capture smooth, gradual structural breaks in the long-run relationship without requiring the researcher to know or specify the break date in advance.

Fourier OLS

Fourier OLS is an OLS regression extended by adding low-frequency trigonometric (sine and cosine) terms to the regressor matrix. These Fourier components approximate smooth, gradual structural changes in the regression relationship over time without requiring knowledge of the number, timing, or form of the breaks.

Fourier Panel Data Analysis

Fourier panel data analysis embeds trigonometric sine and cosine terms into a standard panel regression to approximate smooth, gradual structural shifts in the data-generating process. Rather than assuming a sharp break at a known date, the Fourier approach lets the data reveal the timing and shape of any structural ch

Fourier PP unit root test

The Fourier PP unit root test extends the classical Phillips-Perron test by embedding low-frequency Fourier terms in the deterministic component, enabling the test to account for an unknown number of smooth, gradual structural breaks in the level or trend without pre-specifying their timing or shape.

Fourier Quantile-on-Quantile Regression

Fourier quantile-on-quantile regression extends the quantile-on-quantile (QQ) framework of Sim and Zhou (2015) by embedding Fourier trigonometric terms into the local linear quantile model. This allows the estimated dependence between the quantiles of one variable and the quantiles of another to vary smoothly over time

Fourier SARIMA model

The Fourier SARIMA model extends the classical Seasonal ARIMA framework by incorporating trigonometric (Fourier) terms as deterministic regressors. This allows the model to approximate smooth, complex, or multiple-frequency seasonal patterns without requiring a full seasonal ARIMA structure for every frequency, making

Fourier SVAR Model

The Fourier SVAR model integrates Fourier series approximations into the structural VAR framework, allowing the model to capture smooth, gradual structural breaks and time-varying dynamics in multivariate time series without requiring a priori knowledge of break dates. It recovers structural shocks and their propagatio

Fourier system GMM

Fourier system GMM embeds Fourier trigonometric terms into the System GMM estimator of Blundell and Bond (1998) to accommodate smooth, gradual structural breaks in dynamic panel data. By adding sine and cosine components as regressors, the estimator captures unknown, potentially multiple regime shifts without requiring

Fourier TGARCH

The Fourier TGARCH model extends the Threshold GARCH framework by embedding Fourier trigonometric terms in the conditional variance equation to capture smooth, gradual structural breaks in volatility dynamics. It jointly models asymmetric leverage effects — where negative shocks amplify volatility more than positive sh

Fourier Toda-Yamamoto Causality

The Fourier Toda-Yamamoto (FTY) causality test extends the classical Toda-Yamamoto procedure by embedding Fourier trigonometric terms in the augmented VAR to capture smooth, gradual structural breaks in the deterministic component. It retains the key advantage of the Toda-Yamamoto approach — Granger causality can be te

Fourier VAR model

The Fourier VAR model extends the standard Vector Autoregression by replacing fixed deterministic terms with Fourier trigonometric components, allowing the intercept (and optionally the trend) to shift gradually and smoothly over time. This eliminates the need to pre-specify the number, timing, or shape of structural b

Fourier VECM

The Fourier VECM augments the classical vector error correction model with low-frequency trigonometric terms — sine and cosine components — to capture smooth, gradual structural change in cointegrating relationships without specifying the number or timing of breaks in advance. It is used for multivariate cointegrated s

Fourier WLS

Fourier WLS is a time-series regression technique that embeds low-frequency Fourier trigonometric terms into a Weighted Least Squares framework to capture smooth, gradual structural breaks in means or trends without requiring the researcher to pre-specify their location, timing, or number.

Fourier Zivot-Andrews test

The Fourier Zivot-Andrews test extends the classic Zivot-Andrews (1992) unit root test by replacing sharp, single structural break dummies with a low-frequency Fourier approximation, allowing the test to accommodate smooth, gradual, and multiple unknown breaks in the level or trend of a series.

FRAIL

The FRAIL Scale is a brief, five-item clinical screening tool developed by John E. Morley and colleagues to identify frailty in older adults. Designed as a simple and efficient alternative to more comprehensive frailty assessments, it incorporates the key domains of the frailty phenotype: fatigue, resistance, ambulatio

Frailty Model

The shared frailty model, introduced by Vaupel, Manton, and Stallard in 1979, extends standard survival regression by incorporating a random effect — the 'frailty' — that captures unobserved heterogeneity among subjects or clusters. When survival outcomes are measured on individuals who share a common environment (pati

Frees Test

The Frees test, introduced by Edward Frees in 1995, is a non-parametric diagnostic procedure for detecting cross-sectional dependence in panel data. It is designed for settings where N (number of units) is large and T (time periods) is moderate, making it a standard pre-estimation check before applying panel regression

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