#### Abstract

Inference about the finite population total from probability-proportional-to-size (PPS) samples is considered. In previous work (Zheng and Little, 2003), penalized spline (p-spline) nonparametric model-based estimators were shown to generally outperform the Horvitz-Thompson (HT) and generalized regression (GR) estimators in terms of the root mean squared error. In this article we develop model-based, jackknife and balanced repeated replicate variance estimation methods for the p-spline based estimators. Asymptotic properties of the jackknife method are discussed. Simulations show that p-spline point estimators and their jackknife standard errors lead to inferences that are superior to HT or GR based inferences. This suggests that nonparametric model-based prediction approaches can be successfully applied in the finite population setting by avoiding strong parametric assumptions.

#### Disciplines

Design of Experiments and Sample Surveys | Statistical Methodology | Statistical Models | Statistical Theory

#### Suggested Citation

Zheng, Hui and Little, Rod, "Inference for the Population Total from Probability-Proportional-to-Size Samples Based on Predictions from a Penalized Spline Nonparametric Model" (August 2003). *The University of Michigan Department of Biostatistics Working Paper Series.* Working Paper 9.

http://biostats.bepress.com/umichbiostat/paper9

#### Previous Versions

#### Included in

Design of Experiments and Sample Surveys Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons