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条件分位数约束下参数回归模型的一致非参数检验AI 解读

This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is…

未知形式异方差下的自相关检验AI 解读

This paper develops a test of autocorrelation in the presence of heteroskedasticity of unknown form in the nonlinear regression model. The test statistic is based on the sample autocovariance of the residuals standardized by a nonparametric kernel estimate of the unknown heteroskedasticity function. Under appropriate conditions, the test statistic is shown to have a limiting chi-square distribution. Local power and consistency results for the test are also established. Monte…

混合效应平滑样条方差分析AI 解读

Summary We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a…

稳定化筛式抽样：点估计量分析AI 解读

A modification of sieve sampling is proposed that returns a constant sample size. It is a scheme that selects line items with probability proportional to size (PPS) and nearly without replacement. An unbiased estimator of the total error amount is presented and its variance derived. Conditions under which the scheme is more efficient than sieve sampling and than PPS with replacement sampling are given.

从生命表到风险率：变换方法AI 解读

We address the problem of estimating hazard rates from lifetable data. The central issue is a discretisation bias, which is caused by the aggregation of lifetimes which occurs in lifetable data. Smoothing raw mortalities directly derived from lifetable data leads to severe biases whenever the true hazard rate is large. We propose here a new transformation of smoothed lifetable data which is superior to previous approaches. This is demonstrated by means of large-sample…

以设计点局部重心重新定位的核平滑器AI 解读

The local linear smoother usually gives better performance than the Nadaraya-Watson smoother. An exception is the case of data sparsity. Here we discuss a modification of the Nadaraya-Watson smoother by Müller & Song (1993), based on a horizontal shift of the kernel weights towards the local centre of mass of the design points. This gives performance similar to the local linear when that works well and better performance when it does not. The new smoother also preserves…

杂记：周期图平滑的简易窗口宽度选择器AI 解读

One approach to estimating the spectral density of a stationary time series is to smooth the periodogram and one important component of this approach is the choice of the span for smoothing. This note proposes a new span selector which is based on unbiased risk estimation. The proposed span selector is simple, and does not impose strong conditions on the unknown spectrum. For example, it does not require the unknown spectrum to possess a second derivative, which is a typical…

长程相关误差下核回归的带宽选择AI 解读

We investigate the effect of long-range dependence on bandwidth selection for kernel regression with the plug-in method of Herrmann, Gasser & Kneip (1992). A new bandwidth estimator is proposed to allow for long-range dependence. Properties of the proposed estimator are investigated theoretically and via simulation. We find that the proposed estimator performs well in terms of integrated squared error of the estimated trend, allowing us to incorporate both deterministic…

一般变换模型中具有根号n收敛率的非参数估计AI 解读

We propose simple estimators for the transformation function $\Lambda$ and the distribution function F of the error for the model $$\Lambda (Y) = \alpha + \mathbf{X} \mathbf{\beta} + \varepsilon.$$ It is proved that these estimators are consistent and can achieve the unusual $n^{-1/2}$ rate of convergence on any finite interval under some regularity conditions. We show that our estimators are more attractive than another class of estimators proposed by Horowitz. Interesting…

非参数函数估计中的超效率AI 解读

Fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems (e.g., nonparametric density or regression estimation). In this context several forms of superefficiency can occur. In contrast to what can happen in regular parametric problems, here every parameter point (e.g., unknown density or regression function) can be a point of superefficiency. We begin with an example which shows how fixed parameter asymptotic statements…

分段凸函数估计：初步估计量AI 解读

Given noisy data, function estimation is considered when the unknown function is known a priori to be either convex or concave on each of a small number of regions where the function. When the number of regions is unknown, the model selection problem is to determine the number of convexity change points. For kernel estimates in Gaussian noise, the number of false change points is evaluated as a function of the smoothing parameter. To insure that the number of false convexity…

论筛法与惩罚法AI 解读

We develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates (MLE's) in parametric, semiparametric and nonparametric models. We find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices: the degree of smoothness of the functional and the local size of the underlying parameter space. We show that when the local size of…

The problem of optimal adaptive estimation of a function at a given point from noisy data is considered. Two procedures are proved to be asymptotically optimal for different settings. First we study the problem of bandwidth selection for nonparametric pointwise kernel estimation with a given kernel. We propose a bandwidth selection procedure and prove its optimality in the asymptotic sense. Moreover, this optimality is stated not only among kernel estimators with a variable…

非渐近通用平滑参数、核复杂度与 Yatracos 类AI 解读

We introduce a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the $L_1$ error of the corresponding kernel estimate is not larger than three times the error of the estimate with the optimal smoothing factor plus a constant times $\sqrt{\log n/n}$, where n is the sample size, and the constant depends only on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is…

用于偏最小二乘回归的加性样条AI 解读

This article introduces a generalization of the partial least squares regression (PLS). Transforming the predictors by means of spline functions is a useful way to extend PLS into nonlinearity and to obtain a multiresponse additive model. We describe both statistical and computational aspects of this new method, termed additive splines partial least squares (ASPLS). The performance of ASPLS compared with other PLS methods is illustrated with chemical and physiological…

非参数二元回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

基于核方法的混合密度非参数估计AI 解读

Editor's note: This manuscript was first submitted in May 1996, and a first review with a request for revision was completed in September 1996. Costas Goutis lost his life in a scuba diving accident in July 1996. The associate editor, Jianqing Fan, graciously offered to carry out the required revisions. This article presents a method for estimating the latent distribution of a mixture model. The method is motivated by the standard kernel density estimation, but instead of…

基于粗糙度度量的拟合优度检验AI 解读

A test for the one-sample goodness-of-fit problem is proposed. The test is based on a distance that measures the difference, in terms of roughness, between the underlying density function and the hypothesized density function. One advantage of using a roughness measure is high power in detecting high-frequency alternatives and densities with sharp features. The test statistic that estimates the distance is derived from the viewpoint of kernel density estimation, and a…

随机删失观测下风险函数估计的半参数方法AI 解读

One method for estimating the hazard function is to use a parametric estimator, provided that the underlying distribution of the data can be assumed to belong to some well known family of distributions depending on an unknown, possibly vector-valued parameter. Another approach is to use nonparametric estimators, such as Cox's proportional hazard models, kernel hazard estimators, and so on. However, nonparametric estimators are less efficient than suitably chosen parametric…

核不完全已知的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

多参数似然模型中的局部多项式估计AI 解读

The nonparametric regression technique of local polynomial fitting is extended to multiparameter likelihood models. Some well-known appealing features of local polynomial smoothers, such as the behavior at the boundary, are shown to carry over to the multiparameter case. Asymptotic consistency and normality of the resulting estimators are derived under suitable regularity conditions. This work is motivated by the need for a nonparametric alternative to parametric…

非参数反卷积的非线性平滑EM密度估计与自动平滑选择AI 解读

We study a nonparametric deconvolution density estimation problem. The estimator is obtained by an EM algorithm for a smoothed maximum likelihood estimation problem, which has a unique continuous solution. We present an implementation of the procedure incorporating a data-driven discrepancy principle for selecting the smoothing parameter. Simulations illustrate the good properties of the resulting estimator when the unknown distribution is smooth and has regularly varying…

用于偏最小二乘回归的加性样条AI 解读

This article introduces a generalization of the partial least squares regression (PLS). Transforming the predictors by means of spline functions is a useful way to extend PLS into nonlinearity and to obtain a multiresponse additive model. We describe both statistical and computational aspects of this new method, termed additive splines partial least squares (ASPLS). The performance of ASPLS compared with other PLS methods is illustrated with chemical and physiological…

非参数二维回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…