Outline of statistics

The following outline is provided as an overview of and topical guide to statistics: Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.

Nature of statistics Statistics can be described as all of the following:

An academic discipline: one with academic departments, curricula and degrees; national and international societies; and specialized journals. A scientific field (a branch of science) – widely recognized category of specialized expertise within science, and typically embodies its own terminology and nomenclature. Such a field will usually be represented by one or more scientific journals, where peer reviewed research is published. A formal science – branch of knowledge concerned with formal systems. A mathematical science – field of science that is primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statistics, for example, is mathematical in its methods but grew out of political arithmetic which merged with inverse probability and grew through applications in the social sciences and some areas of physics and biometrics to become its own separate, though closely allied, field.

History of statistics History of statistics Founders of statistics History of probability Timeline of probability and statistics

Describing data Descriptive statistics Average Mean Median Mode Measures of dispersion

Variance Standard deviation Median absolute deviation Correlation Polychoric correlation Outlier Statistical graphics Histogram Frequency distribution Quantile Survival function Failure rate Scatter plot Bar chart

Experiments and surveys Design of experiments Optimal design Factorial experiment Restricted randomization Repeated measures design Randomized block design Cross-over design Randomization Statistical survey Opinion poll

Sampling Sampling theory Sampling distribution Stratified sampling Quota sampling Cluster sampling Biased sample Spectrum bias Survivorship bias

Analysing data Regression analysis Outline of regression analysis Analysis of variance (ANOVA) General linear model Generalized linear model Generalized least squares Mixed model Elastic net regularization Ridge regression Lasso (statistics) Survival analysis Density estimation Kernel density estimation Multivariate kernel density estimation Time series Time series analysis Box–Jenkins method Frequency domain Time domain Multivariate analysis Principal component analysis (PCA) Factor analysis Cluster analysis Multiple correspondence analysis Nonlinear dimensionality reduction Robust statistics Heteroskedasticity-consistent standard errors Newey–West estimator Generalized estimating equation Bootstrapping (statistics) Statistical classification Metric learning Generative model Discriminative model Online machine learning Cross-validation (statistics)

Filtering data Recursive Bayesian estimation Kalman filter Particle filter Moving average SQL

Statistical inference Statistical inference Mathematical statistics Likelihood function Exponential family Fisher information Sufficient statistic Ancillary statistic Minimal sufficiency Kullback–Leibler divergence Nuisance parameter Order statistic Bayesian inference Bayes' theorem Bayes estimator Prior distribution Posterior distribution Conjugate prior Posterior predictive distribution Hierarchical bayes Empirical Bayes method Frequentist inference Statistical hypothesis testing Null hypothesis Alternative hypothesis P-value Significance level Statistical power Type I and type II errors Likelihood-ratio test Wald test Score test Sequential probability ratio test Uniformly most powerful test Exact test Confidence interval Prediction interval Decision theory Optimal decision Type I and type II errors Decision rule Minimax Loss function Mean squared error Mean absolute error Estimation theory Estimator Bayes estimator Maximum likelihood Trimmed estimator M-estimator Minimum-variance unbiased estimator Consistent estimator Efficiency (statistics) Completeness (statistics) Non-parametric statistics Nonparametric regression Kernels Kernel method Statistical learning theory Rademacher complexity Vapnik–Chervonenkis dimension Probably approximately correct learning

Probability distributions Probability distribution Symmetric probability distribution Unimodal probability distribution Conditional probability distribution Probability density function Cumulative distribution function Characteristic function List of probability distributions

Random variables Random variable Central moment L-moment Algebra of random variables

Probability theory Probability Conditional probability Law of large numbers Central limit theorem Concentration inequality Convergence of random variables

Computational statistics Computational statistics Markov chain Monte Carlo Bootstrapping (statistics) Jackknife resampling Integrated nested Laplace approximations Nested sampling algorithm Metropolis–Hastings algorithm Importance sampling Mathematical optimization Convex optimization Linear programming Linear matrix inequality Quadratic programming Quadratically constrained quadratic program Second-order cone programming Semidefinite programming Newton-Raphson Gradient descent Conjugate gradient method Mirror descent Proximal gradient method Geometric programming

Statistics software List of statistical packages

Statistics organizations List of academic statistical associations List of national and international statistical services

Statistics publications List of statistics journals List of important publications in statistics

Persons influential in the field of statistics List of statisticians

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