vekting

Vekting is a statistical and analytical technique in which different observations, variables, or outcomes are assigned weights to reflect their relative importance, frequency, or reliability. The weights alter how data contribute to summaries, models, or decisions, producing results that better represent the population or phenomenon of interest when unweighted analyses would be biased or inefficient.

In survey sampling, vekting adjusts for the sampling design and nonresponse so that estimates are representative of the target population. In statistics, weighted statistics include the weighted mean and the weighted variance, while in regression analysis, weighted least squares applies weights to minimize a weighted sum of squared residuals.

Common weighting schemes include: frequency weights, where a value represents repeated observations; analytic weights, where weights are proportional to the inverse of the observation variance; and inverse probability weights, used to correct for unequal selection probabilities. In data science and machine learning, sample weights address class imbalance or emphasize certain observations during training; propensity score weighting can reduce confounding in observational studies.

Calculation examples: the weighted mean equals the sum of w_i x_i divided by the sum of w_i. In regression, Weighted Least Squares solves the minimization of the sum w_i (y_i − ŷ_i)^2.

Caveats and considerations: choosing weights is critical, and misspecified weights can bias results or inflate variance. Weights should be justified and subjected to sensitivity analyses. Normalization of weights is often used to keep the effective sample size interpretable and to stabilize computations.