Statistical Estimation & Hypothesis Testing

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Abstractions about estimating unknown quantities and testing statistical claims under sampling variability. They cover likelihood and information, exact and asymptotic tests, error measures, nuisance parameters, resampling, variance reduction, sequential analysis, and threats such as spurious relationships.

35 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Brown–Forsythe test — A robust test of equality of group variances obtained by applying one-way ANOVA to absolute deviations from group medians.
• Consistency (statistics) — An asymptotic property in which a statistical estimator, test, interval, or other procedure approaches the correct target or decision as sample information grows.
• Control variates — A Monte Carlo variance-reduction method that adjusts an estimator using correlated quantities whose expectations are known.
• Correspondence analysis — A dimension-reduction and visualization method for contingency tables using chi-square geometry to jointly map row and column profiles.
• Empirical likelihood — A nonparametric likelihood method that assigns probabilities to observed sample points and maximizes their product subject to estimating-equation constraints.
• Empirical probability — An event-probability estimate given by its observed relative frequency in a finite sample of trials.
• Exact test — A hypothesis test whose null distribution and resulting type-I error control are derived without an asymptotic approximation under the stated sampling model.
• Exchangeable random variables — A finite or infinite sequence whose joint probability law is invariant under every finite permutation of its indices.
• Faulty generalization — An informal fallacy that infers a broad population claim from evidence too small, biased or unrepresentative to warrant that scope.
• Fisher information — The expected squared score, or negative expected log-likelihood curvature under regularity conditions, measuring local sensitivity of a probability model to its parameter.
• Generalized p-value — A nuisance-parameter-controlled tail probability derived from a generalized pivotal quantity for testing hypotheses lacking a conventional exact pivot.
• Invariant estimator — An estimator whose output transforms compatibly with a group action applied to both data and parameter space.
• K-statistic — A symmetric unbiased estimator of a population cumulant constructed from sample power sums.
• Likelihood principle — The proposition that, for a fixed statistical model, all sample evidence about its parameters is contained in the observed-data likelihood up to proportionality.
• Linear belief function — A Dempster–Shafer belief-function representation for continuous variables in which evidence is encoded by linear equations with normal residual uncertainty.
• Maximal information coefficient — A normalized statistic searching over bounded grid partitions to measure potentially nonlinear association between two variables.
• Maximum likelihood estimation — Parameter estimation by selecting the model value that makes the observed data most likely under a specified statistical family.
• Mean absolute error — The arithmetic mean of absolute differences between paired predictions or estimates and corresponding observed or reference values.
• Monte Carlo integration — A numerical-integration method estimating an integral from randomized samples and reporting sampling uncertainty that typically decreases with the square root of sample count.
• Normality test — A statistical diagnostic or hypothesis test assessing whether observed data are compatible with a normal-distribution model.
• Nuisance parameter — A model parameter not itself of inferential interest but necessary to account for when estimating or testing the target parameter.
• Orthogonality principle — The condition that a minimum-mean-square estimation error is orthogonal to every admissible variation or estimator-measurable function.
• Oversampling and undersampling in data analysis — Resampling strategies that alter class frequencies in a dataset by adding or repeating minority observations or removing majority observations.
• Paired difference test — A statistical location test applied to within-pair differences when two measurements are linked by subject, unit, match, or repeated observation.
• Pivotal quantity — A function of observed data and unknown model parameters whose sampling distribution is independent of every unknown parameter.
• Qualitative variation — The dispersion of observations across nominal categories, measured by indices that compare concentration in one category with diversity or evenness across categories.
• Sampling error — The difference between a sample statistic and the corresponding population parameter caused by observing only a sample.
• Score test — A likelihood-based hypothesis test using the score gradient and information matrix evaluated at the null-constrained parameter estimate.
• Sequential analysis — Statistical inference in which data are evaluated as they arrive and sampling stops according to a predeclared evidence rule rather than a fixed sample size.
• Spurious relationship — An observed association that does not represent the inferred causal link because coincidence, common cause, trend or selection generates the pattern.
• Standard error — The standard deviation of a statistic's sampling distribution, quantifying how much the statistic would vary across repeated samples under the stated design and model.
• T-statistic — A standardized statistic equal to an estimate’s departure from a hypothesized value divided by its estimated standard error.
• Testing hypotheses suggested by the data — The invalid reuse of the same observations both to select a hypothesis and to test it as though the test had been specified independently.
• Variance reduction — A family of Monte Carlo design changes that lowers estimator variance for a fixed computational budget while preserving the target quantity under stated conditions.
• Wald test — A hypothesis test comparing an unrestricted parameter estimate with a constrained null value using its estimated covariance as a precision weight.