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易处理且可解释的四参数圆周单峰分布族AI 解读

This article presents a class of four-parameter distributions for circular data that are unimodal, possess simple characteristic and density functions and a tractable distribution function, can be interpretably parameterized directly in terms of their trigonometric moments, afford a very wide range of skewness and kurtosis, envelop numerous interesting submodels including the wrapped Cauchy and cardioid distributions, allow straightforward parameter estimation by both method…

与 Möbius 变换相关的圆周分布族及其应用AI 解读

We propose a family of four-parameter distributions on the circle that contains the von Mises and wrapped Cauchy distributions as special cases. The family is derived by transforming the von Mises distribution via a Möbius transformation, which maps the unit circle onto itself. The densities in the family have a symmetric or asymmetric, unimodal or bimodal shape, depending on the values of the parameters. Conditions for unimodality are explored. Further properties of the…

双曲正弦—反双曲正弦分布族AI 解读

We introduce the sinh-arcsinh transformation and hence, by applying it to a generating distribution with no parameters other than location and scale, usually the normal, a new family of sinh-arcsinh distributions. This four-parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution. The central place of the normal distribution in this family affords likelihood ratio tests of…

支撑集位于对角线上方的多元分布AI 解读

A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the…

t 分布的偏斜扩展及其应用AI 解读

Summary A tractable skew t-distribution on the real line is proposed. This includes as a special case the symmetric t-distribution, and otherwise provides skew extensions thereof. The distribution is potentially useful both for modelling data and in robustness studies. Properties of the new distribution are presented. Likelihood inference for the parameters of this skew t-distribution is developed. Application is made to two data modelling examples.

局部似然密度估计AI 解读

This paper considers a class of local likelihood methods introduced by Eguchi and Copas. Unified asymptotic results are presented in the usual smoothing context of the bandwidth, h, tending to zero as the sample size tends to infinity. We present our results pointwise in the univariate case, but then go on to extend them to global properties and to indicate how to cope with the multivariate case. Specific members of the class due to Copas, and Hjort and Jones are seen to be…

相关密度型最小散度估计量的比较AI 解读

This paper compares the minimum divergence estimator of Basu et al. (1998) to a competing minimum divergence estimator which turns out to be equivalent to a method proposed from a different perspective by Windham (1995). Both methods can be applied for any parametric model and contain maximum likelihood as a special case. Efficiencies are compared under model conditions, and robustness properties are studied. Overall the two methods are found to perform quite similarly. Some…

摘要暂缺

偏倚函数未知时基于有偏样本的非参数密度估计AI 解读

We present a kernel estimator for the density of a variable when sampling probabilities depend on that variable. Both the density and sampling bias weight functions are unknown and are estimated nonparametrically. To achieve this, the method requires that two independent samples be taken from a fixed finite population. An estimator of population size follows simply from our density estimator. Asymptotic bias and standard errors for these estimators are provided, and the…

边界处密度函数的改进估计量AI 解读

We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outperform an earlier generalized reflection idea. It also has overall advantages over boundary kernel methods and a nonnegative…

局部线性分位数回归AI 解读

In this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting. Two such estimators are considered. One is based on localizing the characterization of a regression quantile as the minimizer of E{pp (Y — a)|X = x}, where ρp is the appropriate “check” function. The other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters, rather than one. Our aim is to present fully…

高阶偏差核密度估计方法的比较AI 解读

We consider many kernel-based density estimators, all theoretically improving bias from O(h 2), as the smoothing parameter h → 0, to O(h 4). Examples include higher-order kernels, variable kernel methods, and transformation and multiplicative bias-correction approaches. We stress the similarities between what appear to be disparate approaches. In particular, we show how the mean squared errors of all methods have the same form. Our main practical contribution is a…

局部参数化的非参数密度估计AI 解读

This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x, \theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel-smoothed likelihood function which, for each x, can be used to estimate the best local parametric approximant to the true density. This leads to a new density estimator of the form $f(x, \hat{\theta}(x))$, thus inserting the best local parameter estimate for each new value of…

密度估计带宽选择简述AI 解读

There has been major progress in recent years in data-based bandwidth selection for kernel density estimation. Some “second generation” methods, including plug-in and smoothed bootstrap techniques, have been developed that are far superior to well-known “first generation” methods, such as rules of thumb, least squares cross-validation, and biased cross-validation. We recommend a “solve-the-equation” plug-in bandwidth selector as being most reliable in terms of overall…

密度估计的一种简单偏差缩减方法AI 解读

A new method for bias reduction in nonparametric density estimation is proposed. The method is a simple, two-stage multiplicative bias correction. Its theoretical properties are investigated, and simulations indicate its practical potential. The method is easy to compute and to analyse, and extends simply to multivariate and other estimation problems.

核型回归估计量的不同形式及其关系AI 解读

We explore the aims of, and relationships between, various kernel-type regression estimators. To do so, we identify two general types of (direct) kernel estimators differing in their treatment of the nuisance density function associated with regressor variable design. We look at the well-known Gasser-Müller, Nadaraya-Watson, and Priestley-Chao methods in this light. In the random design case, none of these methods is totally adequate, and we mention a novel (direct) kernel…

二元核密度估计中平滑参数化的比较AI 解读

The basic kernel density estimator in one dimension has a single smoothing parameter, usually referred to as the bandwidth. For higher dimensions, however, there are several options for smoothing parameterization of the kernel estimator. For the bivariate case, there can be between one and three independent smoothing parameters in the estimator, which leads to a flexibility versus complexity trade-off when using this estimator in practice. In this article the performances of…

一种简单的根号 n 带宽选择器AI 解读

The asymptotically best bandwidth selectors for a kernel density estimator currently require the use of either unappealing higher order kernel pilot estimators or related Fourier transform methods. The point of this paper is to present a methodology which allows the fastest possible rate of convergence with the use of only nonnegative kernel estimators at all stages of the selection process. The essential idea is derived through careful study of factorizations of the pilot…

长度偏倚数据的核密度估计AI 解读

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems…

核密度估计的一种可靠数据驱动带宽选择方法AI 解读

SUMMARY We present a new method for data-based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the…

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…

长度偏倚数据的核密度估计AI 解读

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems…

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…

非参数回归中的自适应 M 估计AI 解读

A method for robust nonparametric regression is discussed. We consider kernel $M$-estimates of the regression function using Huber's $\psi$-function and extend results of Hardle and Gasser to the case of random designs. A practical adaptive procedure is proposed consisting of simultaneously minimising a cross-validatory criterion with respect to both the smoothing parameter and a robustness parameter occurring in the $\psi$-function. This method is shown to possess a…