Wavelet density estimation for mixing and size-biased data

Wavelet linear density estimation for associated stratified size-biased sample

Ramirez and Vidakovic (2010) considered an estimator of the density function based on wavelets for a random stratified sample from weighted distributions. We extend these results to both positively and negatively associated random variables within strata. An upper bound on Lp-loss for the estimator is given which extends such a result for the L2-consistent given in Ramirez and Vidakovic(2010).

Adaptive Wavelet Estimation of a Biased Density for Strongly Mixing Sequences

Mixing Strategies for Density Estimation

General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under Kullback-Leibler and square L 2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under...

A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data

Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...

Online wavelet-based density estimation for non-stationary streaming data

There has been an important emergence of applications in which data arrives in an online time-varying fashion (e.g. computer network traffic, sensor data, web searches, ATM transactions) and it is not feasible to exchange or to store all the arriving data in traditional database systems to operate on it. For this kind of applications, as it is for traditional static database schemes, density es...