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删失回归数据的后验计算AI 解读

This article describes the computation of and sampling from the posterior density for censored regression problems with normal and generalized log-gamma errors. The data augmentation algorithm (Tanner and Wong 1987) is facilitated in the normal error case because of the form of the augmented posterior. In the generalized log-gamma context, this simplicity is absent. The work of Sweeting (1981) is used as a motivation to develop an importance sampling scheme to sample from an…

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基于广义 Mann–Whitney 统计量的概率置信区间与容忍域AI 解读

Inference procedures are proposed for any specified function of two random variables f(X, Y), assuming that independent random samples from the X and Y populations are available. A generalization of the Mann-Whitney statistic is used to obtain point and interval estimates for the probability that f(X, Y) falls in a given interval. One proposed confidence interval is a modification and improvement to the approach of Halperin, Gilbert, and Lachin (1987) for estimating Pr(X <…

检验简单有序备择的单侧学生化极差检验AI 解读

Consider the usual balanced one-way fixed effects analysis of variance (ANOVA) model X ij = μ i + ε ij (1 ≤ j ≤ n; 1 ≤ i ≤ k), where the ε ij are independent N(0, [sgrave]2) random variables and μ i is the mean of the ith treatment (1 ≤ i ≤ k). The μ i and [sgrave] 2 are unknown parameters. Let X i be the sample mean of the ith treatment based on n observations (1 ≤ i ≤ k), and let S 2 be an unbiased estimate of [sgrave]2, which is distributed independently of the X i as a…

广义线性模型中的不完全数据AI 解读

This article examines incomplete data for the class of generalized linear models, in which incompleteness is due to partially missing covariates on some observations. Under the assumption that the missing data are missing at random, it is shown that the E step of the EM algorithm for any generalized linear model can be expressed as a weighted complete data log-likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range.…

利用正交级数指数形式进行密度估计AI 解读

If a density is represented as an exponential of a series of orthogonal polynomials, it has a simple likelihood with a complete set of sufficient statistics. To ensure that the maximum likelihood equations are well conditioned, the polynomials should be orthogonal with respect to the estimated density. The optimal number of terms in the series can be determined by minimizing an estimate of a loss function. The penalized likelihood equations can be solved with little extra…

相关误差数据的核平滑AI 解读

Kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y = f(x) + ε, where f(x) is a smooth deterministic mean function and ε is an error process with mean zero. In this article, the mean squared error of kernel estimators is computed for processes with correlated errors, and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence. The standard techniques for bandwidth…

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预测区域的校准AI 解读

Suppose that the variable X to be predicted and the learning sample Yn that was observed have a joint distribution, which depends on an unknown parameter θ. The parameter θ can be finite- or infinite-dimensional. A prediction region Dn for X is a random set, depending on Yn , that contains X with prescribed probability α. This article studies methods for controlling simultaneously the conditional coverage proability of Dn , given Yn , and the overall (unconditional) coverage…

缺少群不变性假设时随机化检验的表现AI 解读

Fisher's randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions. For example, the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations. On the other hand, Fisher's randomization construction is not applicable in this example…

时间序列回归中 Durbin–Watson 等不变检验统计量分布的快速计算AI 解读

A method is given for evaluating p values in O(n) operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals. The best known of these is the Durbin-Watson statistic, although several others have been discussed in the literature. The method is numerically exact in the sense that the user specifies the error tolerance at the outset. As with existing exact methods, the problem is…

含替代预测变量模型的近似拟似然估计AI 解读

We consider quasi-likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error. We review and extend four approaches to estimation in this problem, all of them based on small measurement error approximations. A taxonomy of the data sets likely to be available in measurement error studies is developed. An asymptotic theory based on this taxonomy is obtained and includes measurement error and Berkson error models…

利用同期短时间序列预测技术替代AI 解读

It has been shown in the literature that the data of technological substitutions exhibit a strong correlation across different time periods, that is, a strong serial correlation. Significant improvement in predicting such substitutions has been achieved by incorporating serial correlation and power transformation parameters into four growth curve models. The modified models, or data-based transformed models, however, break down when the number of time points is small. This…

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多项概率估计中的辅助统计量悖论AI 解读

Let X be a multinomial (n, p) variable, where n is an ancillary statistic. In Section 2, it is shown that the minimax estimator of p for fixed sample size n is not minimax for squared error loss. In Section 3, it is shown that the minimax estimator of p for fixed sample size n is still minimax for relative squared error loss.

三个正态总体均值多重比较检验的功效AI 解读

This article gives theoretical reasons for the findings of a simulation study by Shaffer (1981). Two well-established procedures for multiple comparison of three normal means are compared—an F procedure and an R procedure. It turns out that for a large set of parameters the average number of rejected pairwise hypotheses is larger when the F procedure is applied. To achieve our result we have to prove a special instance of a conjecture by David, Lachenbruch, and Brandis…

非高斯回归模型中的自适应样条平滑AI 解读

A convenient and efficient algorithm for penalized likelihood smoothing spline regression is proposed and illustrated. The amount of smoothing is tuned adaptively via the generalized cross-validation method. Under certain conditions, the method is shown to approximately minimize the expected Kullback-Leibler discrepancy in modeling one-parameter exponential family observations through the canonical parameter. The algorithm is applied to fit logistic models using interaction…

多行观测对矩阵条件数影响的评估AI 解读

Given a matrix X of n observations on k variables, it is known that the singular values of X can change substantially when few rows are omitted from X. Hadi (1988) shows that no general closed-form equation can relate the singular values of X to the singular values of X with one row deleted and gives closed-form approximations to the relationship between the singular values of the two matrices. In this article, we extend Hadi's results to the more general case of…

指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

采用广义Mantel–Haenszel估计量的列联表齐性检验AI 解读

A conditional test for the homogeneity of the odds ratios in L2 × K (K > 2) tables is developed based on a multiple hypergeometric distribution. The test is a generalization of the Breslow-Day test (1980) and is useful in sparse tables. For computational feasibility, the conditional maximum likelihood estimator is replaced by a consistent but inefficient estimator in the test statistic. If this is the case, it is shown that the asymptotic distribution is not chi squared, as…

尺度的稳健L估计及其天文学应用AI 解读

In this article, we investigate the robustness properties of a class of L estimators of scale and then develop robust procedures for making inferences about scale. We pay particular attention to trimmed estimators that should perform well when the underlying model is Gaussian. We find that trimmed versions of the efficient linear L estimator for the Gaussian distribution perform better than trimmed standard deviation estimators. We then apply a trimmed version of the…

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EM 算法的蒙特卡洛实现与简易数据增广算法AI 解读

The first part of this article presents the Monte Carlo implementation of the E step of the EM algorithm. Given the current guess to the maximizer of the posterior distribution, latent data patterns are generated from the conditional predictive distribution. The expected value of the augmented log-posterior is then updated as a mixture of augmented log-posteriors, mixed over the generated latent data patterns (multiple imputations). In the M step of the algorithm, this…

揭示被掩蔽的多元异常值与杠杆点AI 解读

Detecting outliers in a multivariate point cloud is not trivial, especially when there are several outliers. The classical identification method does not always find them, because it is based on the sample mean and covariance matrix, which are themselves affected by the outliers. That is how the outliers get masked. To avoid the masking effect, we propose to compute distances based on very robust estimates of location and covariance. These robust distances are better suited…