Parametriarviot

Parametriarviot, or parameter estimates, are numerical values derived from data that aim to approximate unknown characteristics of a population. In statistics, a parameter is a fixed but unknown quantity describing the population, while an estimator is a rule or formula that uses sample data to produce an estimate of that parameter.

Common estimation methods include maximum likelihood estimation (MLE), the method of moments, least squares, and Bayesian estimation. MLE selects parameter values that maximize the likelihood of observing the given data. Least squares minimizes the sum of squared residuals between observed and fitted values. The method of moments matches sample moments (such as the sample mean and variance) to theoretical population moments. Bayesian estimation combines a prior distribution with the data to form a posterior distribution, from which point estimates (for example the posterior mean or median) may be derived.

Estimator properties describe how estimates behave across repeated samples. An unbiased estimator has an expected value equal to the true parameter; consistency means it converges to the true parameter as sample size grows; efficiency concerns the estimator’s variance. Inference uses estimates together with measures of uncertainty, such as standard errors, confidence intervals, and hypothesis tests.

Practical considerations include identifiability, model misspecification, data quality, and outliers. Regularization methods (such as ridge or lasso) can improve estimation in the presence of many parameters or multicollinearity by trading some bias for lower variance.