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随机模型中方差分量函数的同时置信区间AI 解读

Interval estimation of certain functions of variance components is of interest to research workers in all fields of applications in which the variance component model is used. Confidence intervals for linear functions and ratios of variance components have been proposed by several authors. For the most part, these intervals are approximate with unknown exact probabilities associated with their coverage. In this article a technique is given for the construction of…

时间自相关下设计的稳健性（二）：一阶自回归过程的最优性与数值结果AI 解读

The optimum design and its efficiency relative to the uniform design for estimating the mean of a stationary First-order autoregressive process plus an independent error are characterized completely. This is related to the work of Jones (1948), Optimum designs and variances of least squares estimates are calculated numerically for the problem of estimating the slope in a simple linear regression when the errors follow the above structure, for a range of values of the sample…

混合线性模型的最佳线性递归估计AI 解读

Recursive estimation techniques for fixed and completely random models are extended to mixed linear models. The Kalman filter is used to obtain recursive estimators for a two-part random model where the second random factor obeys a generalized autoregressive process. By passing to the limit in an appropriate way, recursions for the mixed model are derived.

不依赖坐标的岭回归界AI 解读

The dependence of ridge-regression estimates on the choice of parameterization is defined with reference to the hull of all possible ridge estimates for all possible parameterizations. A reanalysis of Hoerl and Kennard's (1970) 10-factor example and Marquardt and Snee's (1975) acetylene data reveals that most conclusions depend on the parameterization.

投影寻踪回归AI 解读

A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, does not require the definition of a metric in the predictor space, and lends itself to graphical interpretation.

多元时间序列建模及应用AI 解读

An approach to the modeling and analysis of multiple time series is proposed. Properties of a class of vector autoregressive moving average models are discussed. Modeling procedures consisting of tentative specification, estimation, and diagnostic checking are outlined and illustrated by three real examples.

利用岭回归估计营销中的直接滞后效应AI 解读

A prediction criterion for ridge regression is developed and used for estimating lagged effect patterns by means of the direct lag model. As examples, the Lydia Pinkham monthly and annual data are analyzed, showing that lag patterns can be obtained that are in agreement across time intervals.

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非线性联立模型工具变量估计量的比较研究AI 解读

In the context of single equation approaches to the estimation of nonlinear simultaneous models, three classes of estimators can be established, using different fitted values established by a stage-one regression. The first uses the Fitted values of the nonlinear function in the second-stage regression. The second, called here the naive instrument, substitutes a fitted value inside the nonlinear function. The third uses an estimate of the conditional expectation of the…

基于子样本的一般单样本非参数检验统计量AI 解读

A general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations. The test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m = 1 and a modified Wilcoxon signed-rank test statistic for m = 2. Asymptotic normality of properly standardized versions of our statistics is established under general conditions. Small sample…

有序分类列联表独立性检验的渐近功效与效率AI 解读

Asymptotic power formulas for tests of independence against simple association models in I × J contingency tables with ordered categories are presented. Yates's score correlation test and Spearman's tied rank correlation test are compared with a likelihood ratio test proposed by S. J. Haberman for testing independence in log-linear models with ordered classifications. Asymptotic power and relative efficiencies are derived under local alternatives that need not be included in…

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条件独立列联表中边际均值的推断AI 解读

Consider a three-way contingency table with factors A, B, and C. Assume factors A and B are independent for each given level of factor C. Inference procedures concerning the marginal means of the levels of factor A are studied. Maximum likelihood estimators, unbiased estimators, and uniformly minimum variance unbiased estimators are obtained. Exact variance formulas for the estimators are obtained. Large sample theory is developed and used for testing and confidence…

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相关样本下 Kruskal–Wallis 检验的渐近保守性与效率AI 解读

The robustness (asymptotic conservativeness) of Kruskal-Wallis test under certain departures from mutual independence of K univariate samples is established. This robustness provides a procedure for testing the equality of K marginal distribution functions on a broken random sample from a K-variate distribution which satisfies a mild condition. For the unbroken sample, a generalized Kruskal-Wallis test is proposed for testing the symmetry of a K-dimensional distribution…

分段回归的一种新最大似然算法AI 解读

This paper presents a piecewise regression method for continuous models containing max or min operators, or both. This method does not require knowledge of the zone in which a shift in regimes occurs. Moreover, it allows the application of analytical derivatives to maximize the likelihood function, which greatly simplifies the estimation of the model. The method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables.

截断参数空间中线性不变估计量的不可容许性AI 解读

Estimation problems are considered where the actual parameter space is a strict subset of the full parameter space. A linear invariance structure is assumed and a quadratic loss function is used. Then it is shown that estimators taking values near the boundary of the parameter space are inadmissible and better estimators are presented. Applications are given in the fields of inequality constraint regression and randomized response.

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不依赖坐标表示的岭回归界AI 解读

The dependence of ridge-regression estimates on the choice of parameterization is defined with reference to the hull of all possible ridge estimates for all possible parameterizations. A reanalysis of Hoerl and Kennard's (1970) 10-factor example and Marquardt and Snee's (1975) acetylene data reveals that most conclusions depend on the parameterization.

多项分布拟合优度似然比统计量的矩与分布近似AI 解读

Approximations were derived for the mean and variance of G 2, the likelihood ratio statistic for testing goodness of fit in a k cell multinomial distribution. These approximate moments, accurate to O(N -3), may be used in fitting the distribution of G 2. Extensive numerical studies of the exact and approximate distributions were performed in the special case of equiprobability. The asymptotic chi-squared distribution was found to fit poorly for k ≥ 4. Satisfactory results…

学生化极差检验的一种多元对应形式AI 解读

It is well known that T max 2 test procedure, a multivariate analog of studentized range test, can be derived by using Roy's union intersection principle with a bilinear decomposition of the MANOVA hypothesis that is response-wise infinite and contrastwise finite. In this article an alternative union intersection derivation of T max 2 test is presented using the matrix decomposition of the MAN-OVA hypothesis. This decomposition is responsewise as well as contrastwise…