On Wavelet Estimation of the Derivatives of a Density Based on Biased Data

Abstract

Here, we consider wavelet based estimation of the derivatives of a probability density function under random sampling from a weighted distribution and extend the results regarding the asymptotic convergence rates under the i.i.d. setup studied in Prakasa Rao (1996) to the biased-data setup. We compare the performance of the wavelet based estimator with that of the kernel based estimator obtained by differentiating the Efromovich (2004) kernel density estimator through a simulation study.

Keywords:

• Besov spaces
• Derivatives of density estimation
• Biased Data
• Wavelet
• Weighted distribution.

Mathematics Subject Classifications:

• Primary 62G07
• secondary 62G20.