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非参数回归的自动带宽选择与置信区间AI 解读

In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the $\sqrt{n}$-consistent bandwidth selector of Härdle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator $\hat{m}_g$. Then we consider classical confidence intervals based on kernel…

短程与长程相关误差下非参数回归的带宽选择AI 解读

We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number,…

众数估计中 L^p 误差的最小化AI 解读

We show that, for $L^p$ convergence of the mode of a nonparametric density estimator to the mode of an unknown probability density, finiteness of the pth moment of the underlying distribution is both necessary and sufficient. The basic requirement of existence of finite variance has been overlooked by statisticians, who have earlier considered mean square convergence of nonparametric mode estimators; they have focussed on mean squared error of the asymptotic distribution,…

局部最小二乘回归的带宽选择方法AI 解读

Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local…

通过小波收缩适应未知光滑度AI 解读

We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: A threshold level is assigned to each dyadic resolution level by the principle of minimizing the Stein unbiased estimate of risk (Sure) for threshold estimates. The computational effort of the overall procedure is order N · log(N) as a function of the…

在曲线样本中寻找结构特征AI 解读

The shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema, inflection points, and so on. When analyzing a sample of regression curves, it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample. Such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the…

用于质量改进的注射器分级：非参数回归方法AI 解读

In the biomedical products industry, measures of the quality of individual clinical specimens or manufacturing production units are often available in the form of high-dimensional data such as continuous recordings obtained from an analytical instrument. These recordings are then examined by experts in the field who extract certain features and use these to classify individuals. To formalize and quantify this procedure, an approach for extracting features from recordings…

用于注射器质量改进分级的非参数回归方法AI 解读

In the biomedical products industry, measures of the quality of individual clinical specimens or manufacturing production units are often available in the form of high-dimensional data such as continuous recordings obtained from an analytical instrument. These recordings are then examined by experts in the field who extract certain features and use these to classify individuals. To formalize and quantify this procedure, an approach for extracting features from recordings…

精确消费者剩余与无谓损失的非参数估计AI 解读

The authors apply nonparametric regression models to estimation of demand curves of the type most often used in applied research. From the demand curve estimators they derive estimates of exact consumers surplus and deadweight loss. The authors also develop tests of the symmetry and downward sloping properties of compensated demand. They work out asymptotic normal sampling theory for kernel and series nonparametric estimators as well as for the parametric case. The paper…

非参数标记依赖风险率模型中的核估计AI 解读

We introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker. We establish the pointwise and global convergence of our estimator.

全局泛函的非参数估计与回归协变量解释力度量AI 解读

In a nonparametric regression setting with multiple random predictor variables, we give the asymptotic distributions of estimators of global integral functionals of the regression surface. We apply the results to the problem of obtaining reliable estimators for the nonparametric coefficient of determination. This coefficient, which is also called Pearson's correlation ratio, gives the fraction of the total variability of a response that can be explained by a given set of…

回归模型两侧的非参数变换AI 解读

SUMMARY One way to model heteroscedasticity and skewness of the error distribution in regression is to transform both sides of the regression equation. If it is possible to transform the regression equation to result in normally distributed errors, then we can obtain more efficient parameter estimates and valid prediction intervals. One problem with this approach is that the choice of transformation is usually restricted to the power or shifted power family. Often there is…

多元判别分析与最大惩罚似然密度估计AI 解读

SUMMARY A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f, where B is a stochastic operator and π is the raw histogram. Then, we investigate the…

异方差误差下线性回归的同时置信带AI 解读

The Scheffé method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current…

含噪图像中真实灰度级数量、取值及相对频率的估计AI 解读

In some applications information is presented as a two-dimensional image corrupted by random noise. Due to the precision of the equipment that forms the image, we can typically have a large number, v, of observed gray levels. But in many situations we know that the number of true gray levels, p, corresponding to, for example, the number of tissue types in a brain slice, is much less than v. In this article we propose a method based on the kernel density estimator for…

噪声图像中真实灰度级数量、取值与相对频率的估计AI 解读

In some applications information is presented as a two-dimensional image corrupted by random noise. Due to the precision of the equipment that forms the image, we can typically have a large number, v, of observed gray levels. But in many situations we know that the number of true gray levels, p, corresponding to, for example, the number of tissue types in a brain slice, is much less than v. In this article we propose a method based on the kernel density estimator for…

异方差误差下线性回归的同时置信带AI 解读

The Scheffé method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current…

变换核密度估计量的渐近性质AI 解读

An asymptotic expansion is provided for the transformation kernel density estimator introduced by Ruppert and Cline. Let $h_k$ be the band-width used in the $k$th iteration, $k = 1,2,\ldots, t$. If all bandwidths are of the same order, the leading bias term of the $l$th derivative of the $t$th iterate of the density estimator has the form $\bar{b}^{(l)}_t(x) \pi^t_{k=1} h^2_k$, where the bias factor $\bar{b}_t(x)$ depends on the second moment of the kernel $K$, as well as on…

作为局部平滑器的样条AI 解读

A smoothing spline is a nonparametric curve estimate that is defined as the solution to a minimization problem. One problem with this representation is that it obscures the fact that a spline, like most other nonparametric estimates, is a local, weighted average of the observed data. This property has been used extensively to study the limiting properties of kernel estimates and it is advantageous to apply similar techniques to spline estimates. Although equivalent kernels…

多维有序稀疏列联表的几何组合估计AI 解读

A geometric combination estimator is proposed for $d$-dimensional ordinal contingency tables. The proposed estimator is nonnegative. It is shown that, assuming sufficient smoothness and boundary conditions for the underlying probabilities, the rate of convergence of mean summed squared error (MSSE) of this estimator is $O(K^{-1}N^{-8/(d+8)})$ for $d$-dimensional tables $(d \leq 4)$ with $K$ cells and sample size $N$. This rate is optimal under the smoothness assumptions, and…

半参数广义线性模型中的渐近有效估计AI 解读

We use the method of maximum likelihood and regression splines to derive estimates of the parametric and nonparametric components of semiparametric generalized linear models. The resulting estimators of both components are shown to be consistent. Also, the asymptotic theory for the estimator of the parametric component is derived, indicating that the parametric component can be estimated efficiently without under-smoothing the nonparametric component.

分位数回归模型渐近协方差矩阵估计的蒙特卡洛研究AI 解读

This Monte Carlo study examines several estimation procedures of the asymptotic covariance matrix in the quantile and censored quantile regression models: design matrix bootstrap, error bootstrapping, order statistic, sigma bootstrap, homoskedastic kernel, and heteroskedastic kernel. The Monte Carlo samples are drawn from two alternative data sets: (a) the unaltered Current Population Survey (CPS) for 1987 and (b) this CPS data with independence between error term and…

局部多项式拟合的数据驱动带宽选择：可变带宽与空间适应AI 解读

SUMMARY When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important issue of how to select the smoothing parameter or bandwidth. In the case of estimating curves with a complicated structure, a variable bandwidth is desirable. Furthermore, the bandwidth should be indicated by the data themselves. Recent developments in nonparametric smoothing…

长程依赖下的密度估计AI 解读

Dehling and Taqqu established the weak convergence of the empirical process for a long-range dependent stationary sequence under Gaussian subordination. We show that the corresponding density process, based on kernel estimators of the marginal density, converges weakly with the same normalization to the derivative of their limiting process. The phenomenon, which carries on for higher derivatives and for functional laws of the iterated logarithm, is in contrast with…