Weighted Least Squares Estimation with Sampling Weights

A set of unweighted normal equations for a least squares solution assumes that the response variable of each equation is equally reliable and should be treated equally. When there is a reason to expect higher reliability in the response variable in some equations, we use weighted least squares (WLS) to give more weight to those equations. For an analysis of survey data, sampling weights, as relatively important variables, should be used for unbiased and efficient estimates. We will briefly go over the least squares theory and related issues and propose a specific form of “weight” variable when we apply the sampling weights to the weighted equations. Data from the National Health and Nutrition Examination Survey (NHANES), a periodic survey conducted by the National Center for Health Statistics (NCHS), Centers for Disease Control and Prevention (CDC) will be analyzed to demonstrate the proposed approach.