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含脉冲时间序列的非高斯模型AI 解读

A non-Gaussian autoregressive-like model is presented for time series that exhibit occasional large increases in value, termed pulses, and exponential decay between pulses. The model differs from a first-order autoregressive process in its incorporation of feedback between the distribution of the current innovation and the history of the process. Likelihood-based methods of inference for the model are developed, and an application to endocrinological data is given.

无交互双因素模型中秩变换统计量的效能AI 解读

To test for treatment effects in a two-way model when the classical assumptions of normality of errors and constancy of variance cannot be verified, Hora and Conover (1984) proposed a rank test in which the entire data set is ranked, the ranks are scored, and then the classical analysis of variance F statistic is applied to the scored ranks. They showed that the limiting null distribution of this test statistic is a chi-squared distribution divided by its degrees of freedom.…

通过非参数混合推广逻辑回归AI 解读

Logistic regression is a common technique for analyzing the effect of a covariate vector x on the number of successes y in m trials when y has a binomial distribution. But at times either the logistic curve does not describe the probability of success p(x) adequately, or m is larger than 1 and y is more variable than the binomial distribution allows. Overdispersion relative to the binomial distribution is possible if the m trials in a set or “litter” are positively…

核估计的局部带宽选择AI 解读

A kernel estimate of a curve that uses an adaptive procedure for local selection of the bandwidth is considered here. A two-step procedure is proposed for estimating the local bandwidth that minimizes the mean squared error (MSE) of a kernel estimator for nonparametric regression. First, a consistent estimate of the exact MSE is constructed. Then the bandwidth that minimizes the estimate of the MSE is calculated. Sufficient conditions under which this bandwidth is…

二元符号检验AI 解读

In this article the bivariate location problem is treated. New appealing bivariate analogs of the univariate sign tests are proposed for testing the null hypothesis concerning the unknown symmetry center. These tests remain unaltered under any nonsingular linear transformation. From these promising findings a whole family of locally most powerful invariant sign tests is introduced. The tests proposed earlier (Blumen 1958; Hodges 1955) are specific members of this family. For…

检验参数是否随时间保持不变AI 解读

Tests are proposed for detecting possible changes in parameters when the observations are obtained sequentially in time. While deriving the tests the alternative one has in mind specifies the parameter process as a martingale. The distribution theory of these tests relies on the large-sample results; that is, only the limiting null distributions are known (except in very special cases). The main tool in establishing these limiting distributions is weak convergence of…

预测分布的最优报告AI 解读

Consider a problem in which you and a group of other experts must report your individual predictive distributions for an observable random variable X to some decision maker. Suppose that the report of each expert is assigned a prior weight by the decision maker and that these weights are then updated based on the observed value of X. In this situation you will try to maximize your updated, or posterior, weight by appropriately choosing the distribution that you report,…

正态均值线性不等式假设的一致更强检验AI 解读

This article considers some hypothesis-testing problems regarding normal means. In these problems, the hypotheses are defined by linear inequalities on the means. We show that in certain problems the likelihood ratio test (LRT) is not very powerful. We describe a test that has the same size, α, as the LRT and is uniformly more powerful. The test is easily implemented, since its critical values are standard normal percentiles. The increase in power with the new test can be…

Jackknife 方差估计近似的效率与一致性AI 解读

The problem considered is the computation reduction for general delete-d jackknife variance estimators. The delete-d jackknife estimator was proved consistent (Shao and Wu 1986), and in this article its mean squared error is shown to have order o(n –2), where n is the sample size. These properties are not shared by the traditional delete-1 jackknife in some situations. Use of the delete-d jackknife, however, requires ( n d ) recomputations of a point estimate θ, which…

Hellinger 偏差检验：效率、崩溃点与实例AI 解读

Hellinger distance analogs of likelihood ratio tests are proposed for parametric inference. The proposed tests are based on minimized Hellinger distances between nonparametric density estimates and densities corresponding to null and unconstrained parametric models. If the parametric model is correct, the Hellinger deviance test is asymptotically equivalent to the likelihood ratio test. A simulation study examines the relative performance of these tests in finite samples.…

模型隐含假设对参数推断的影响AI 解读

In choosing a model, there are important considerations beyond the goodness of fit, namely that the subsequent inferences should not rely on questionable assumptions implicit in the model, because otherwise they will be suspect. The two-parameter lognormal distribution provides an example. The symmetry on the log scale leads to the anomaly that relative frequencies of classes in the lower tail can substantially affect inferences on the upper tail. This is contrary to the…

使用 Bootstrap 构造分布函数置信带AI 解读

We first discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling but do not assume that F is continuous. The known alternative approach is to use the quantiles from the tabled Kolmogorov distribution. This approach is known to be conservative. It has already been shown in Bickel and Freedman (1981) that the bootstrap confidence band has the correct coverage probability asymptotically. We show by…

用条件似然方法分析重复分类测量AI 解读

This article presents a method for analyzing repeated measures with categorical responses based on maximizing a conditional likelihood. Many existing methods for analyzing repeated categorical responses, such as those proposed by Duncan (1980, 1985), Bishop, Fienberg, and Holland (1975), and Cochran (1950) are special cases of the method based on the conditional likelihood approach. This article explores the relationships among the various methods and extends several of the…

季节调整的敏感性分析：实证案例研究AI 解读

Three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior. Analyses are performed within a semi-Bayesian framework where inferences for target quantities of interest, such as seasonally adjusted values, are obtained as posterior distributions conditional on observed data and fitted parameter values. Such an approach is similar to previous model-based methods of seasonal…

不完全修复系统的可靠性估计AI 解读

This study of statistical inference for repairable systems focuses on the development of estimation procedures for the life distribution F of a new system based on data on system lifetimes between consecutive repairs. The Brown—Proschan imperfect-repair model postulates that at failure the system is repaired to a condition as good as new with probability p, and is otherwise repaired to the condition just prior to failure. In treating issues of statistical inference for this…

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小域估计：条件分析AI 解读

In estimating means, totals, and other parameters for small domains of a finite population, the survey statistician is usually faced with a domain sample size that is random rather than controlled at the selection stage. Often a sensible approach is to make design-based inference conditionally on the realized sample size in the domain (nd ). In this article, we suggest and analyze some small domain estimators and their design-based conditional confidence intervals. The…

分层抽样中的最小方差估计AI 解读

This article discusses efficiency properties of some common stratified estimators, in the context of a superpopulation model, relative to the greatest lower bound on the variance of the Horvitz—Thompson estimator. The estimators discussed use both Dalenius—Hodges and model-based survey sampling (MBSS) stratification and a variety of sample allocation methods, including optimum, proportionate, and uniform sample allocation. The main result is that both Dalenius—Hodges…

自相关线性模型中普通最小二乘法的效率AI 解读

This article provides a reconsideration of Kramer's (1980) results on least squares estimation in linear models with autocorrelated errors. Kramer's results are shown to be dependent on his measure of efficiency and to understate the advantages of correcting for autocorrelation.

协方差结构对平衡随机参数增长曲线模型方差估计的影响AI 解读

Intuition suggests that altering the covariance structure of a parametric model for repeated-measures data alters the variances of the model's estimated mean parameters. The purpose of this article is to sharpen such intuition for a family of growth-curve models with differing numbers of random effects for the individual sampling units and with a fixed structure on the mean. For every member of this family, the maximum likelihood (ML) estimator of the fixed effects is…

门限自回归过程的检验与建模AI 解读

The threshold autoregressive model is one of the nonlinear time series models available in the literature. It was first proposed by Tong (1978) and discussed in detail by Tong and Lim (1980) and Tong (1983). The major features of this class of models are limit cycles, amplitude dependent frequencies, and jump phenomena. Much of the original motivation of the model is concerned with limit cycles of a cyclical time series, and indeed the model is capable of producing…

一般相关均值下的成对比较AI 解读

A commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means μi (1 ≤ i ≤ k) for certain experimental designs. One way to do this, the T method proposed by Tukey (1953), constructs simultaneous confidence intervals for all pairwise differences of the treatment means μi – μj (1 ≤ i, j ≤ k, i ≈ j). The joint confidence level of these confidence intervals, however, depends in a very complicated…