Wavelet linear density estimation for associated stratified size-biased sample
- 11 April 2012
- journal article
- research article
- Published by Taylor & Francis in Journal of Nonparametric Statistics
- Vol. 24 (2) , 429-445
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.Keywords
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