View Submission - EcoSta2022

A0429
**Title: **Asymmetric kernel density estimation for biased data
**Authors: **Yoshihide Kakizawa - Hokkaido University (Japan) **[presenting]**

**Abstract: **For the data supported on $[0,\infty)$ or $[0,1]$, the so-called boundary bias problem is one of the interests, and asymmetric kernel density estimation has been well studied. We consider a situation where a random sample $\{ X_1,\ldots,X_n \}$ is not directly available but the data $\{ Y_1,\ldots,Y_n \}$ is instead observed from the length-biased distribution. Some previous works have been discussed without care of the boundary bias problem of the Rosenblatt-Parzen kernel density estimator. Indeed, an usual approximation (near the origin $x=0$) of a certain smooth function $g$ as the convolution integral does not hold when $g(0)>0$, and that, even for the case $g(0)=0$, the order of the approximation (near the origin $x=0$) is slower when $g'(0) \neq 0$, This is the motivation that, instead of the location-scale kernel $k((x-\cdot)/h)/h$, we focus on an application of an asymmetric kernel, and then propose two density estimators.