Wavelet linear density estimation for associated stratified size-biased sample
by Dr. Hassan Doosti
Abstract: We focus our attention on the estimation of a density function with stratified random variables from weighted distributions. We consider two generalisations of the results of Ramirez and Vidakovic (2010), Wavelet Density Estimation for Stratified Size-Biased Sample, Journal of Statistical Planning and Inference, 140, 419 - 432. In the first case, we adopt the same framework as that of Ramirez and Vidakovic (2010) but replace the normalisation parameters by its estimators. Then, we determine the rate of convergence of the modified linear wavelet estimator under the L2-risk over a very rich class of function set: the Besov balls. This completes the L2-consistency proved in Theorem 3.1 of Ramirez and Vidakovic (2010). The second part contains the main contribution of this study; we investigate the L2-performances of the proposed wavelet linear estimator for negatively and positively associated random variables.
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