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单侧交叉验证AI 解读

A new method of selecting the smoothing parameters of nonparametric regression estimators is introduced. The method, termed one-sided cross-validation (OSCV), has the objectivity of cross-validation and statistical properties comparable to those of a plug-in rule. The new method may be viewed as an application of the prequential model selection method of Dawid. As such, our results identify a situation in which the prequential method is a more efficient model selector than…

加性模型拟合的全自动带宽选择方法AI 解读

This article describes a fully automated bandwidth selection method for additive models that is applicable to the widely used backfitting algorithm of Buja, Hastie, and Tibshirani. The proposed plug-in estimator is an extension of the univariate local linear regression estimator of Ruppert, Sheather, and Wand and is shown to achieve the same Op (n –2/7) relative convergence rate for bivariate additive models. If more than two covariates are present, theoretical justification…

利用分箱数据实现密度估计的高阶收敛率AI 解读

A method is proposed for achieving fast—O(n –8/9) and faster—asymptotic mean integrated squared error (AMISE) convergence rates in density estimation using data condensed to standard histogram bin counts and edges. The method involves the two elements of B splines and the correct mass proportions property, in which the probability mass for the histogram bins equals exactly the fraction of the data found in those bins. It is shown that the asymptotic bias of such an estimate…

刚体运动估计的线性模型及其几何质量检验应用AI 解读

A geometrical method to assess the quality of a part is to sample points on the surface of the part and to bring an ideal computer representation of the part as close as possible to the sampled locations. The points are sampled with a coordinate measuring machine (CMM) that gives the coordinates, with respect to the machine's own three-dimensional system of axis, of the sampled locations. Computer-assisted design (CAD) gives the ideal representation of the part. The matching…

摘要暂缺

This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method…

Hilbert 空间值依赖异质数组的中心极限定理与函数中心极限定理及应用AI 解读

We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent…

比例优势回归与筛最大似然估计AI 解读

This paper introduces, under a censoring mechanism, an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method. The procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative Kullback-Leibler risk to select the best approximation. The procedure adapts to various unknown…

具有相关随机误差的平滑样条模型AI 解读

Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are…

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…

局部估计方程AI 解读

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a “parameter” depending on a predictor. The nonparametric component is estimated via local polynomials with loess or kernel weighting; asymptotic theory is derived for the…

稳健二元非参数回归的贝叶斯方法AI 解读

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can…

Triogram：自适应三角剖分模型AI 解读

In this article we introduce the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. We illustrate the technique for bivariate regression and log-density estimation and indicate how our approach can be applied directly to model bivariate functions in the broader context of an extended linear model. The entire estimation procedure is invariant under affine transformations and is a natural approach…

Generalized Linear Models.- Linear Models, Vector Spaces, and Residual Likelihood.- An Assessment of Approximate Maximum Likelihood Estimators in Generalized Linear Models.- Scaled Link Functions for Heterogeneous Ordinal Response Data.- Longitudinal Data Analysis.- Software Design for Longitudinal Data Analysis.- Asymptotic Properties of Nonlinear Mized-Effects Models.- Structured Antedependence Models for Longitudinal Data.- Effect of Confounding and Other Misspecification…

具有相关随机误差的平滑样条模型AI 解读

Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are…

稳健二元非参数回归的贝叶斯方法AI 解读

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can…

Triogram 三角剖分样条模型AI 解读

In this article we introduce the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. We illustrate the technique for bivariate regression and log-density estimation and indicate how our approach can be applied directly to model bivariate functions in the broader context of an extended linear model. The entire estimation procedure is invariant under affine transformations and is a natural approach…

形状的统计理论AI 解读

1 Introduction.- 1.1 Background of Shape Theory.- 1.2 Principles of Allometry.- 1.3 Defining and Comparing Shapes.- 1.4 A Few More Examples.- 1.4.1 A Simple Example in One Dimension.- 1.4.2 Dinosaur Trackways From Mt. Tom, Massachusetts.- 1.4.3 Bronze Age Post Mold Configurations in England.- 1.5 The Problem of Homology.- 1.6 Notes.- 1.7 Problems.- 2 Background Concepts and Definitions.- 2.1 Transformations on Euclidean Space.- 2.1.1 Properties of Sets.- 2.1.2 Affine…

弱依赖数据下的筛极值估计AI 解读

Many non/semiparametric time series estimates may be regarded as different forms of sieve extremum estimates. For stationary absolute regular mixing observations, the authors obtain convergence rates of sieve extremurn estimates and root-n asymptotic normality of 'plug-in' sieve extremum estimates of smooth functionals. As applications to time series models, they give convergence rates for nonparametric ARX(p,q) regression via neural networks, splines, wavelets; root-n…

非参数回归中部分交叉验证、GCV 与随机化 GCV 的渐近比较AI 解读

When using nonparametric estimates of the mean curve, surface or image underlying noisy observations, the selection of "smoothing parameters" is generally crucial. This paper gives a theoretical comparison of the performances of generalized cross-validation (GCV) and of its fast randomized version (RGCV), as selection criteria. This is mainly done by studying the asymptotic distribution of the excess error for each selector, that is, the difference between the (data-driven)…

非平稳时间序列平滑的筛自助法AI 解读

We propose a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on nonparametric trend estimation and autoregressive approximation for some noise process. The bootstrap scheme itself does i.i.d. resampling of estimated innovations from fitted autoregressive models. We show the validity and indicate second-order correctness of such sieve bootstrap approximations for the limiting distribution of nonparametric…

多元回归的投影估计及其在函数型 ANOVA 模型中的应用AI 解读

A general theory on rates of convergence of the least-squares projection estimate in multiple regression is developed. The theory is applied to the functional ANOVA model, where the multivariate regression function is modeled as a specified sum of a constant term, main effects (functions of one variable) and selected interaction terms (functions of two or more variables). The least-squares projection is onto an approximating space constructed from arbitrary linear spaces of…

条件对称性的一致设定检验AI 解读

This paper presents a consistent specification test of conditional symmetry using a kernel method. The test statistic is shown to be asymptotically distributed as standard normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distribution. Power against local alternatives is also investigated. A Monte Carlo simulation is provided to evaluate the finite-sample performance of the test.

误差修正模型的自适应估计AI 解读

This paper considers adaptive maximum likelihood estimation of reduced rank vector error correction models. It is shown that such models can be asymptotically efficiently estimated even in the absence of knowledge of the shape of the density function of the innovation sequence, provided that this density is symmetric. The construction of the estimator, involving the nonparametric kernel estimation of the unknown density using the residuals of a consistent preliminary…