American Statistical Association New York City Metropolitan Area Chapter New York State Psychiatric Institute at Columbia University Medical Center Biostatistics Seminar

Unequal probability sampling designs are commonly employed in data collection by science and government, in an effort to obtain better estimates or make sampling more efficient. When the sample is selected with unequal probability, the sample quantiles are no longer unbiased estimates of the population quantiles. To obtain an unbiased estimate, the sample is often weighted using the inverse of selection probability. The sample-weighted method is valid with large sample sizes historically common in population-based probability samples. However, the asymptotic assumption for large samples yields limited guidance when the sample is small, as is increasingly the case, as small area or small domain estimation become more popular. When design information is available to modelers, it can be used to predict the non-sampled values based on a statistical model relating the outcome variables to the design information. We proposed two Bayesian model-based estimators for finite population quantiles that are robust to model misspecification, where inferences are based on the posterior predictive distribution of the non-sampled values. We showed by simulation studies that the Bayesian model-based methods yield smaller root mean squared errors than the sample-weighted estimator. When sample size is small, the 95% credible intervals of the two new Bayesian methods have closer to the nominal level confidence coverage than the sample-weighted estimator.

Qixuan Chen received her Ph.D. in Biostatistics from the University of Michigan in 2009 and is now an Assistant Professor in the Department of Biostatistics at Columbia University. Her research interests involve the development of statistical methods for complex survey data and data with missing values. She is currently working on the Bayesian model-based methods for survey samples and the variable selection methods for multiply imputed data. Her applied interests are broad, including mental health, environmental epidemiology, and the social sciences.