Parametric statistics

Parametric statistics uses probability models described by a finite-dimensional set of parameters to analyze data, estimate quantities, or test hypotheses.

Probability distribution: A mathematical description of the possible values of a random variable and their probabilities. Parametric methods begin by choosing a distributional form for the data.
Maximum likelihood estimation: A method that estimates model parameters by maximizing the likelihood of observed data. It is a standard way to fit parametric models to observations.
Nonparametric statistics: Statistical methods that avoid specifying a fixed finite-dimensional family for the data distribution. It reduces reliance on a particular distributional form when that form is uncertain.
Linear regression: A model that represents a response as a linear function of predictors plus an error term. With specified error assumptions, it is a central parametric model for relationships between variables.
Model misspecification: A condition in which the assumed statistical model does not adequately represent the data-generating process. Incorrect distributional or structural assumptions can distort parametric estimates and uncertainty.
Statistical model: A set of probability distributions used to represent how data may have been generated. Parametric statistics is one family of statistical models, distinguished by finite-dimensional parameterization.
Method of moments: An estimation method that matches sample moments to corresponding moments implied by a model. It provides a direct alternative to likelihood-based parameter estimation.
Semiparametric model: A statistical model with both a finite-dimensional parameter and an unrestricted or infinite-dimensional component. It occupies a middle ground between fully specified parametric models and nonparametric methods.
Logistic regression: A regression model for categorical outcomes that links predictors to outcome probabilities through the logistic function. Its finite coefficients parameterize conditional probabilities for binary or categorical outcomes.
Goodness of fit: An assessment of how closely a statistical model's predictions or distributions match observed data. Fit checks help identify whether a chosen parametric family represents the observations adequately.

Linked from 2 pages

Family (statistics)Narrower topic: Families commonly underpin parametric methods, but the terms describe different things.