The Kernel Estimate is Relatively Stable
نویسنده
چکیده
Consider the Parzen-Rosenblatt kernel estimate f. = (l/n) ~ Kh (x-Xi), where h > 0 is a constant, K is an absolutely integrable i=1 function with integral one, Kh(X)=(1/ha)K(x/h), and X1 ..... X. are iid random variables with common density f on R d. We show that for all e > 0, n8 2 2 sup P(lSlf.-fl-E~lf.-fll>e)<Ze 32~1KI. whenever liminfl~E~lf,-f]=oo. We also study what happens when h is allowed to depend upon the data sequence.
منابع مشابه
THE COMPARISON OF TWO METHOD NONPARAMETRIC APPROACH ON SMALL AREA ESTIMATION (CASE: APPROACH WITH KERNEL METHODS AND LOCAL POLYNOMIAL REGRESSION)
Small Area estimation is a technique used to estimate parameters of subpopulations with small sample sizes. Small area estimation is needed in obtaining information on a small area, such as sub-district or village. Generally, in some cases, small area estimation uses parametric modeling. But in fact, a lot of models have no linear relationship between the small area average and the covariat...
متن کاملThe Relative Improvement of Bias Reduction in Density Estimator Using Geometric Extrapolated Kernel
One of a nonparametric procedures used to estimate densities is kernel method. In this paper, in order to reduce bias of kernel density estimation, methods such as usual kernel(UK), geometric extrapolation usual kernel(GEUK), a bias reduction kernel(BRK) and a geometric extrapolation bias reduction kernel(GEBRK) are introduced. Theoretical properties, including the selection of smoothness para...
متن کاملHeat Kernel Estimates for Truncated Stable-like Processes and Weighted Poincaré Inequality
In this paper, we investigate pure jump symmetric processes in R whose jumping kernel is comparable to the one for truncated rotationally symmetric α-stable process where jumps of size larger than a fixed number κ > 0 is removed. We establish sharp two-sided heat kernel estimate and derive parabolic Harnack principle for such jump-type processes. Moreover, we show that bounded functions that ar...
متن کاملAsymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data
Kernel density estimators are the basic tools for density estimation in non-parametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paper, we initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...
متن کاملSolving Volterra Integral Equations of the Second Kind with Convolution Kernel
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (2005)] to gain...
متن کامل