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A simple smooth backfitting method for additive models

加性模型的一种简便平滑后拟合方法

In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya–Watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting. Each component is estimated with the same asymptotic accuracy as if the other components were known.

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Bandwidth selection for smooth backfitting in additive models

加性模型平滑回拟合的带宽选择

The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443–1490] is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound. In this paper, we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models. The first one is a penalized least squares approach which is based on higher-order stochastic expansions for the residual sums of…

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New methods for bias correction at endpoints and boundaries

端点与边界估计的平移偏差校正新方法

We suggest two new, translation-based methods for estimating and correcting for bias when estimating the edge of a distribution. The first uses an empirical translation applied to the argument of the kernel, in order to remove the main effects of the asymmetries that are inherent when constructing estimators at boundaries. Placing the translation inside the kernel is in marked contrast to traditional approaches, such as the use of high-order kernels, which are related to the…

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On Estimation of Monotone and Concave Frontier Functions

单调凹前沿函数的估计

Abstract When analyzing the productivity of firms, one may want to compare how the firms transform a set of inputs x (typically labor, energy or capital) into an output y (typically a quantity of goods produced). The economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier, the boundary of the production set. The frontier function gives the maximal level of output attainable by a firm for a given combination of…

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A NOTE ON THE CONVERGENCE OF NONPARAMETRIC DEA ESTIMATORS FOR PRODUCTION EFFICIENCY SCORES

生产效率得分的非参数 DEA 估计量收敛性札记

Efficiency scores of production units are measured by their distance to an estimated production frontier. Nonparametric data envelopment analysis estimators are based on a finite sample of observed production units, and radial distances are considered. We investigate the consistency and the speed of convergence of these estimated efficiency scores (or of the radial distances) in the very general setup of a multi-output and multi-input case. It is shown that the speed of…

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A Cross-Validatory Choice of Smoothing Parameter in Adaptive Location Estimation

自适应位置估计中平滑参数的交叉验证选择

Abstract This article proposes a new data-driven method for selecting the smoothing parameter involved in constructing kernel-based adaptive location estimators. The method consists of minimizing a cross-validatory criterion with respect to the bandwidth occurring in the kernel-type estimators of the efficient score function. It is shown that the location estimator with a data-driven bandwidth selector is indeed an adaptive estimator. A simulation study reveals that the…

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A Cross-Validatory Choice of Smoothing Parameter in Adaptive Location Estimation

自适应位置估计中平滑参数的交叉验证选择

This article proposes a new data-driven method for selecting the smoothing parameter involved in constructing kernel-based adaptive location estimators. The method consists of minimizing a cross-validatory criterion with respect to the bandwidth occurring in the kernel-type estimators of the efficient score function. It is shown that the location estimator with a data-driven bandwidth selector is indeed an adaptive estimator. A simulation study reveals that the method is…

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Comparison of Data-Driven Bandwidth Selectors

数据驱动带宽选择方法的比较

This paper provides a comparison. on three levels. of several promising data-driven methods for selecting the bandwidth of a kernel density estimator. The methods compared are: least squares cross-validation. biased cross-validation. partitioned cross-validation. and a plug-in rule. The levels of comparison are: asymptotic rate of convergence to the optimum, explici t calculation in the case of one target density. and a simulation study. It is seen that the plug-in bandwidth…

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