Wavelet linear density estimation for associated stratified size-biased sample

Abstract

Ramirez and Vidakovic [(2010), ‘Wavelet Density Estimation for Stratified Size-Biased Sample’, Journal of Statistical Planning and Inference, 140, 419–432] considered an estimator of the density function based on wavelets with independent stratified random variables from weighted distributions. They proved that it is L 2-consistent. In this paper, we complete this result by determining the rate of convergence attained by a slightly modified version of their estimator (including an estimator of the normalisation parameters). Then, we explore the case when the random variables are negatively and positively associated within strata. The theory is illustrated with a simulation study.