In this paper we study the estimation of a quantile function based on left truncated and right censored data by the kernel smoothing method. Asymptotic normality and a Berry-Esseen type bound for the kernel quantile estimator are derived. Monte Carlo studies are conducted to compare the proposed estimator with the PL-quantile estimator.

We propose a working independent profile likelihood method for the semiparametric time-varying coefficient model with correlation. Kernel likelihood is used to estimate time-varying coefficient. Profile likelihood for the parametric coefficient is formed by plugging in the nonparametric estimator. For independent data, the estimator is asymptotically normal and achieves the asymptotic semiparam...

Given a sample from a discretely observed compound Poisson process we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. Asymptotic expansions of the bias and variance of the estimator are given and pointwise weak consistency and asymptotic normality are established. We also derive the minimax conve...

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya–Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.

Suppose we have independent observations of a pair of independent random variables, one with a density and the other discrete. The sum of these random variables has a density, which can be estimated by an ordinary kernel estimator. Since the two components are independent, we can write the density as a convolution and alternatively estimate it by a convolution of a kernel estimator of the conti...