Non - Parametric Estimators Which Can Be “ Plugged - In ”
نویسنده
چکیده
University of California at Berkeley and The Hebrew University of Jerusalem ∗†We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the minimax rate of convergence on suitable function spaces, while, at the same time, when “plugged-in”, estimate efficiently (at a rate of n−1/2 with the best constant) many functionals of the object? For example, can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function? We show that this is impossible for very large sets, e.g., expectations of all functions bounded by M < ∞. However we also show that it is possible for sets as large as indicators of all quadrants, i.e., distribution functions. We give appropriate constructions of such estimates.
منابع مشابه
Two-step Smoothing Estimation of the Time-variant Parameter with Application to Temperature Data
‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...
متن کاملAn Application of Non-response Bias Reduction Using Propensity Score Methods
In many statistical studies some units do not respond to a number or all of the questions. This situation causes a problem called non-response. Bias and variance inflation are two important consequences of non-response in surveys. Although increasing the sample size can prevented variance inflation, but cannot necessary adjust for the non-response bias. Therefore a number of methods ...
متن کاملCombining parametric, semi-parametric, and non-parametric survival models with stacked survival models.
For estimating conditional survival functions, non-parametric estimators can be preferred to parametric and semi-parametric estimators due to relaxed assumptions that enable robust estimation. Yet, even when misspecified, parametric and semi-parametric estimators can possess better operating characteristics in small sample sizes due to smaller variance than non-parametric estimators. Fundamenta...
متن کاملDoubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates.
We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widel...
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 کامل