Quasi-maximum Likelihood Estimation with Complex Survey Data

Large-scale surveys such as the Current Population Survey, the Panel Study of Income Dynamics and the Health and Retirement Study use complex sample designs. The resulting data violate the familiar i.i.d. assumption. We need to adjust our statistical practice accordingly. This paper explains how the population means, the population linear regression coeecients, and other population parameter values can be consistently estimated with a survey design commonly used in large-scale surveys, and it derives the asymptotic distributions of the estimators. We also discuss estimation of the asymptotic covariance matrices of the estimators, which is essential in making statistical inferences.