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变系数模型中的平滑样条估计AI 解读

Summary Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian ‘confidence intervals’ are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small…

多项分布数据的拟合优度检验AI 解读

Several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution. The new tests are Neyman smooth-type tests with orders selected adaptively from the data. They are shown, through Fourier and large-sample analyses, to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives. Simulation results and a real example illustrate the finite-sample validity of the…

多项分布数据的拟合优度检验AI 解读

Several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution. The new tests are Neyman smooth-type tests with orders selected adaptively from the data. They are shown, through Fourier and large-sample analyses, to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives. Simulation results and a real example illustrate the finite-sample validity of the…

非参数回归中的可加性检验AI 解读

Additive models are one means of assuaging the curse of dimensionality when nonparametric smoothing methods are used to estimate multivariable regression functions. It is important to have methods for testing the fit of such models, especially in high dimensions where visual assessment of fit becomes difficult. New tests of additivity are proposed in this paper that derive from Fourier series estimators with data-driven smoothing parameters. Other tests related to the…

非参数回归中的置信带AI 解读

New bias-corrected confidence bands are proposed for nonparametric kernal regression. These bands are constructed using only a kernel estimator of the regression curve and its data-selected bandwidth. They are shown to have asymptotically correct coverage properties and to behave well in a small-sample study. One consequence of the large-sample developments is that Bonferroni-type bands for the regression curve at the design points also have conservative asymptotic coverage…

非参数回归中的异方差检测AI 解读

SUMMARY Diagnostic tests and plots are proposed for detecting heteroscedasticity in nonparametric regression. The large and small sample power properties are studied for a class of test statistics for the hypothesis of homogeneous variances. New diagnostic plots are also developed and illustrated.

Cusum、von Neumann 与平滑型拟合优度检验的共同结构AI 解读

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests…

累积和、冯·诺伊曼与基于平滑的拟合优度检验的共同框架AI 解读

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests…

拟合优度检验中 Cramér–von Mises 与非参数函数估计方法的渐近比较AI 解读

Two new statistics for testing goodness-of-fit are derived from the viewpoint of nonparametric density estimation. These statistics are closely related to the Neyman smooth and Cramer-von Mises statistics but are shown to have superior properties both through asymptotic and small sample analyses. Comparison of the proposed tests with the Cramer-von Mises statistic requires the development of a novel technique for comparing tests that are capable of detecting local…

通过阶数选择准则检验回归拟合优度AI 解读

A new test is derived for the hypothesis that a regression function has a prescribed parametric form. Unlike many recent proposals, this test does not depend on arbitrarily chosen smoothing parameters. In fact, the test statistic is itself a smoothing parameter which is selected to minimize an estimated risk function. The exact distribution of the test statistic is obtained when the error terms in the regression model are Gaussian, while the large sample distribution is…

用于多样本问题的 Pearson φ² 距离分量AI 解读

A general approach to the k-sample problem for continuous random variables, based on a generalization of Pearson's classical φ2 measure, is presented. Tests are developed by considering an analysis of variance type of orthogonal decomposition of a distance measure for a k-population goodness-to-fit hypothesis. Estimates of some of these components are shown to provide test statistics for the hypothesis that the k-populations have a common distribution. Several classical…

利用非参数回归检验线性模型的拟合优度AI 解读

This article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model. The large-sample properties of parametric goodness-of-fit tests for linearity are considered. The inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression. Large-sample theory is derived for two variants of this type of statistic. The results demonstrate…

k 样本问题中 Pearson φ² 距离度量的分量AI 解读

Abstract A general approach to the k-sample problem for continuous random variables, based on a generalization of Pearson's classical φ2 measure, is presented. Tests are developed by considering an analysis of variance type of orthogonal decomposition of a distance measure for a k-population goodness-to-fit hypothesis. Estimates of some of these components are shown to provide test statistics for the hypothesis that the k-populations have a common distribution. Several…

多项式—三角回归的曲线拟合AI 解读

We consider a method of estimating an unknown regression curve by regression on a combination of low-order polynomial terms and trigonometric terms. Estimation based on trigonometric functions alone is known to suffer from bias problems at the boundaries due to the periodic nature of the fitted functions. We show that these boundary problems are alleviated by adding low-order polynomial terms. The utility of the method is illustrated with examples, and asymptotic results…

摘要暂缺

由Pearson平方距离分量导出的检验统计量AI 解读

A general approach to the comparison of two absolutely continuous distributions is presented based on Pearson's θ2 measure. Although no simple estimates are available for θ2, it can be decomposed into components, all of which are easily estimated. Asymptotic distribution theory is derived for the component estimates, and the form of the components is considered for several standard problems. It is demonstrated that the components-of-θ2 approach provides a unified approach to…

关于平滑先验与非线性回归的一个注记AI 解读

A generalization of a nonparametric estimator proposed by Shiller (1984) is considered. The estimator is shown to be directly related to penalized least squares estimation and spline smoothing. Some simplifications concerning the computation of Shiller's estimator and corresponding posterior covariances are indicated.

平滑样条的诊断方法AI 解读

SUMMARY Diagnostic measures appropriate for use with smoothing splines are derived and their properties are investigated. The proposed measures focus on detection of observations which substantially influence the fit and provide additional information over that obtained from examination of residuals alone. A numerical example illustrates the technique.

若干时间序列模型的最优与渐近最优设计札记AI 解读

The problem of regression design in the presence of correlated errors is considered. Under the assumption that derivative information is available on the response process, uniqueness results for optimal designs given in Eubank, Smith and Smith (1981) for the BLUE of the regression coefficient are extended to a wider class of processes. In the event that derivatives cannot be sampled, an asymptotic solution is developed and extended to the multiparameter setting.

基于密度—分位数函数的最优间距选择AI 解读

In this paper design techniques for continuous parameter time series regression analysis are employed to develop a general approach to optimal spacing selection for the linear estimation of location and scale parameters by sample quantiles from uncensored or censored samples. The spacings derived from this approach are asymptotically optimal in the sense that they result in near optimal asymptotic relative efficiencies for large values of $k$, the number of spacing elements.…

某些时间序列模型中最优设计的唯一性与最终唯一性AI 解读

Using the results of Barrow, et al., and Chow on the optimal placement of knots in the approximation of functions by piecewise polynomials, we show the uniqueness or "eventual uniqueness" of optimal designs for certain time series models considered by Sacks and Ylvisaker, and Wahba. In addition, the limiting behavior (as the sample size increases) of the variance of the BLUE of the regression coefficient is characterized in terms of the density defining the design, and the…