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核密度估计中最优的数据驱动带宽选择AI 解读

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n−½ where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample…

核密度估计中最优的数据驱动带宽选择AI 解读

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n−½ where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample…

概率密度导数估计的带宽选择AI 解读

SUMMARY An adaptation of least squares cross-validation is proposed for bandwidth choice in the kernel estimation of the derivatives of a probability density. The practicality of the method is demonstrated by an example and a simulation study. Theoretical justification is provided by an asymptotic optimality result.

核分位数估计量AI 解读

For an estimator of quantiles, the efficiency of the sample quantile can be improved by considering linear combinations of order statistics, that is, L estimators. A variety of such methods have appeared in the literature; an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a Guassian kernel, and the bandwidths are identified. It is seen that some implicit choices of the smoothing parameter are asymptotically…

摘要暂缺

回归曲线的半参数比较AI 解读

The comparison of nonparametric regression curves is considered. It is assumed that there are parametric (possibly nonlinear) transformations of the axes which map one curve into the other. Estimation and testing of the parameters in the transformations are studied. The rate of convergence is $n^{-1/2}$ although the nonparametric components of the model typically have a rate slower than that. A statistic is provided for testing the validity of a given completely parametric…

数据驱动带宽选择方法的比较AI 解读

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…

非参数回归中的方差估计AI 解读

A simple explicit estimator of variance in nonparametric regression is suggested, based on the mean square of a sequence of residuals. The estimator is valid for general error distributions, has elementary bias and variance properties, and is optimal to both first and second orders.

密度与强度估计中平滑参数选择器的等价性AI 解读

Kernel smoothing is an attractive method for the nonparametric estimation of either a probability density function or the intensity function of a nonstationary Poisson process. In each case the amount of smoothing, controlled by the bandwidth, that is, smoothing parameter, is crucial to the performance of the estimator. Bandwidth selection by cross-validation has been widely studied in the context of density estimation. A bandwidth selector in the intensity estimation case…

密度估计中的核阶数选择AI 解读

The selection of the order, i.e., number of vanishing moments, of the kernel in a kernel density estimator is considered from two points of view. First, theoretical properties are investigated by a mean integrated squared error analysis of the problem. Second, and perhaps more importantly, cross validation is proposed as a practical method of choice, and theoretical backing for this is provided through an asymptotic optimality result.

自动选择的回归平滑参数距最优值有多远？AI 解读

We address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation. Call the “optimal bandwidth” the minimizer of the average squared error. We consider several automatically selected bandwidths that approximate the optimum. How far are the automatically selected bandwidths from the optimum? The answer is studied theoretically and through simulations. The theoretical results include a central…

摘要暂缺

随机右删失样本核密度估计的渐近最优带宽选择AI 解读

This paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship. First, an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given. Second, it is shown that if the bandwidth is chosen by the data-based method of least-squares cross-validation, then it is asymptotically optimal in a compelling sense. A by-product of the first part is an…

核密度估计带宽选择所固有的噪声AI 解读

In the setting of kernel density estimation, data-driven bandwidth, i.e., smoothing parameter, selectors are considered. It is seen that there is a well-defined, and surprisingly restrictive, bound on the rate of convergence of any automatic bandwidth selection method to the optimum. The method of least squares cross-validation achieves this bound.

密度估计中交叉验证方法的比较AI 解读

In the setting of nonparametric multivariate density estimation, theorems are established which allow a comparison of the Kullback-Leibler and the least-squares cross-validation methods of smoothing parameter selection. The family of delta sequence estimators (including kernel, orthogonal series, histogram and histospline estimators) is considered. These theorems also show that either type of cross validation can be used to compare different estimators (e.g., kernel versus…

摘要暂缺

非参数回归中若干带宽选择方法的渐近非等价性AI 解读

SUMMARY The bandwidth selection problem in nonparametric kernel regression is considered. Bandwidth selectors based on cross-validation and on Akaike's information criterion, atc, and his finite prediction error, FBE, are among those compared. It is seen that they are not necessarily asymptotically equivalent. Conditions are given under which the equivalence holds and modifications are suggested which make the selectors equivalent.