Uniform strong consistency of a frontier estimator using kernel regression on high order moments
نویسندگان
چکیده
We consider the high order moments estimator of the frontier of a random pair, introduced by Girard, S., Guillou, A., Stupfler, G. (2013). Frontier estimation with kernel regression on high order moments. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions. AMS Subject Classifications: 62G05, 62G20.
منابع مشابه
[hal-00764425, v2] Uniform strong consistency of a frontier estimator using kernel regression on high order moments
We consider the high order moments estimator of the frontier of a random pair, introduced by Girard, S., Guillou, A., Stupfler, G. (2013). Frontier estimation with kernel regression on high order moments. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function be...
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 کاملSome Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...
متن کاملStrong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic properties of this estimator depend on the average prediction error of the functional autoregressive function. Sufficient conditions are studied to provide stro...
متن کاملUNIFORM IN BANDWIDTH CONSISTENCY OF KERNEL - TYPE FUNCTION ESTIMATORS By
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.
متن کامل