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可变带宽核密度估计AI 解读

We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two…

密度估计中的最大平滑原则AI 解读

We propose a widely applicable method for choosing the smoothing parameters for nonparametric density estimators. It has come to be realized in recent years (e.g., see Hall and Marron 1987; Scott and Terrell 1987) that cross-validation methods for finding reasonable smoothing parameters from raw data are of very limited practical value. Their sampling variability is simply too large. The alternative discussed here, the maximal smoothing principle, suggests that we consider…

密度估计中的有偏与无偏交叉验证AI 解读

Nonparametric density estimation requires the specification of smoothing parameters. The demands of statistical objectivity make it highly desirable to base the choice on properties of the data set. In this article we introduce some biased cross-validation criteria for selection of smoothing parameters for kernel and histogram density estimators, closely related to one investigated in Scott and Factor (1981). These criteria are obtained by estimating L 2 norms of derivatives…

过度平滑的非参数密度估计AI 解读

The optimal histogram for a sample of size n from a density defined on the entire real line requires at least (2n)1/3 bins, under mild smoothness conditions. Similar bounds exist for the frequency polygon and kernel estimators. Values near these bounds give nearly optimal results for a variety of smooth densities, providing good, quick density estimates.

改进非负核密度估计量的收敛速度AI 解读

To improve the rate of decrease of integrated mean square error for nonparametric kernel density estimators beyond $0(n^{-\frac{4}{5}}),$ we must relax the constraint that the density estimate be a bonafide density function, that is, be nonnegative and integrate to one. All current methods for kernel (and orthogonal series) estimators relax the nonnegativity constraint. In this paper we show how to achieve similar improvement by relaxing the integral constraint only. This is…