Optimal Wavelet Estimation of Density Derivatives for 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).

Wavelet Based Estimation of the Derivatives of a Density for m-Dependent Random Variables

Here, we propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of m−dependent random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for the such estimators.

Wavelet Based Estimation of the Derivatives of a Density for a Discrete-Time Stochastic Process: Lp-Losses

We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...

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...

Adaptive Wavelet Estimation of a Biased Density for Strongly Mixing Sequences