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边际尾概率近似与标量参数推断AI 解读

In many situations, inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density. For such inference, accurate approximations of marginal tail probabilities are useful to avoid high-dimensional integrals. Two tail probability approximations are developed in this paper. Numerical results given for conditional inference in location-scale and linear regression models…

重复次数可能不等且数据非正态时的测定分析方差函数估计AI 解读

Estimation of parametric variance functions using transformations of standard deviations based on replication at each design point is common in, but not limited to, assay analysis. It is shown that ignoring unequal replication can lead to bias and inefficiency in estimation. Efficiency comparisons for different transformations for nonnormal distributions are given. A method to account for bias is described that can offer robustness to nonnormality and leads to a comparison…

广义线性回归的主成分估计AI 解读

The generalized linear model (Nelder & Wedderburn, 1972) has become an elegant and practical option to classical least-squares linear model building. We consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response. It is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique, as an option to traditional maximum…

带宽选择器为何偏向较小带宽及其修正AI 解读

This note is concerned with the problem of automatic data-driven bandwidth selectors for nonparametric regression. Though some selectors were shown to be consistent and asymptotically unbiased by Rice (1984) and Hãrdle, Hall & Marron (1988), it is often observed in simulation studies that most selectors are biased toward undersmoothing. An explanation for this is given. The source of the large sample variation in the bandwidth estimates is also pointed out. This leads to the…

比例风险回归中的解释变异AI 解读

Two new measures of the proportion of the variation of possibly censored survival times explained by a given proportional hazards model are presented. It is shown that the previously suggested proportion of explained log likelihood is not a useful measure of predictive precision. The new measures are intuitively appealing and sufficiently simple for routine application.

失效类型缺失时竞争风险的修正对数秩检验AI 解读

We propose a modified log rank test for the analysis of competing risks survival data, when failure type is missing for some individuals. The proposed test reduces to a standard log rank test when all failure types are known. The test arises from a partial likelihood, constructed under semiparametric assumptions on the relationship between cause-specific hazards.

重捕获调试的似然停止规则AI 解读

Consideration is given to determining when all the faults in a reliability system have been detected, assuming the use of the recapture debugging procedure introduced by Nayak (1988). A stopping rule based on the likelihood ratio is proposed. Compared to the stopping rule suggested by Nayak, this likelihood-based rule makes better use of the available information, and, for a given error level, yields a small reduction in the average time taken to reach a decision. A…

传染病传播模型中接触率的最小二乘估计AI 解读

The contact rate and associated contact number determine the rate of spread of an infectious disease whose population dynamics are described by a mathematical model. It is shown how to obtain least-squares estimates of the contact rate for a standard homogeneous univariate model and a four-group model with different contact rates between the groups. The results of a small scale simulation are presented in the case of the four-group model. It is argued that the least-squares…

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…

线性与二次判别函数的比较AI 解读

Asymptotic expansions of the distributions of the linear and the quadratic discriminant functions are derived. The expected misclassification probabilities of these two functions are compared when the covariance matrices are proportional and the sample sizes are equal. Some numerical experiments are carried out to investigate the relation between the parameters and the boundary point such that if the sample size is smaller than the point the linear discriminant function is…

剖面得分的 Bartlett 偏差校正是一种鞍点校正AI 解读

Bartlett's bias correction to the profile score function is proved equal, to first order, to the leading correction term of the double saddlepoint approximation to the conditional score function in canonical exponential families.

生存分布在指定年龄下的“新优于旧”性质检验AI 解读

The cumulative distribution function F, of a nonnegative random variable, is said to be new better than used of specified age t0 if F¯(x+t0)≤F¯(x)F¯(t0) for all x≥0⁠, where F¯=1-FLet We propose a class of test statistics Tk, indexed by a positive integer k, for testing the null hypothesis that F belongs to A against the alternative hypothesis that F is new better than used of specified age t0 but not in A. We compare the performance of our proposed test statistics with the…

Bootstrap偏差AI 解读

Use of the bootstrap in estimation of the sampling distribution of a pivot is considered for two simple situations. It is shown by a simulation study that in each case the bootstrap is noticeably biased for small sample sizes. The techniques of computer algebra are used to obtain an exact assessment of the bias in both problems and an approximate theoretical analysis based on saddlepoint approximation is presented.

截断时间与失效时间独立性假设的检验AI 解读

For data subject to random censorship, it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically. For data subject to random truncation, however, it is possible to test independence of truncation time and failure time. A statistic generalizing Kendall's tau is proposed for testing the independence assumption, and asymptotic properties under the null hypothesis are derived. A conditional permutation test is…

生存模型中基于鞅的残差AI 解读

Graphical methods based on the analysis of residuals are considered for the setting of the highly-used Cox (1972) regression model and for the Andersen-Gill (1982) generalization of that model. We start with a class of martingale-based residuals as proposed by Barlow & Prentice (1988). These residuals and/or their transforms are useful for investigating the functional form of a covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of…

Wicksell 微粒问题中的核估计AI 解读

We consider the estimation of the probability density function of the radii of spheres in a medium, given the radii of their profiles in a random cross-section. This problem is known as Wicksell's corpuscle problem. We present a new estimator related to the classical kernel density estimator and discuss its properties. A comparison is made with other estimators related to the kernel estimator.

测量误差模型的修正得分函数及其广义线性模型应用AI 解读

Statistical models whose independent variables are subject to measurement errors are often referred to as ‘errors-in-variables models’. To correct for the effects of measurement error on parameter estimation, this paper considers a correction for score functions. A corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables. This approach makes it…

基于模型的统计分析的一般框架AI 解读

This paper presents a general framework for model-based statistics. The framework is based on extended concepts of sufficiency and ancillarity. The fundamental theorem of the new theory exhibits in a single equation the reference distributions for decision theory, model checking, and conditional inference for a general statistical model. The theorem includes the equations upon which Bayesian and frequentist statistics are founded. The general theory also fills two gaps…

利用暴露与结局替代测量设计 Logistic 回归研究AI 解读

Suppose that a binary or polytomous outcome variable is related to a possibly continuous exposure variable through a logistic regression model, and that prior to sample selection subjects can be characterized according to ‘surrogates’ for outcome and exposure. The surrogate variables are assumed to satisfy certain conditional independence properties commonly used in errors-in-variables models. This paper considers the problem of using the surrogate variables to select…

数据平移似然与 Jeffreys 规则AI 解读

According to the definition used by Box & Tiao (1973) for a likelihood to be ‘data translated’ it must have location form in terms of a sufficient statistic. In contrast to Jeffreys's arguments for a uniform prior, theirs does not cover cases such as the Cauchy location family, and is in this sense stronger than the group-theoretic criterion of invariance. Their definition is easily modified to cover such cases through the introduction of an ancillary statistic, and their…

摘要暂缺

失效类型缺失时竞争风险数据的修正对数秩检验AI 解读

We propose a modified log rank test for the analysis of competing risks survival data, when failure type is missing for some individuals. The proposed test reduces to a standard log rank test when all failure types are known. The test arises from a partial likelihood, constructed under semiparametric assumptions on the relationship between cause-specific hazards.

再捕获调试中的似然停止规则AI 解读

Consideration is given to determining when all the faults in a reliability system have been detected, assuming the use of the recapture debugging procedure introduced by Nayak (1988). A stopping rule based on the likelihood ratio is proposed. Compared to the stopping rule suggested by Nayak, this likelihood-based rule makes better use of the available information, and, for a given error level, yields a small reduction in the average time taken to reach a decision. A…

传染病传播模型中接触率的最小二乘估计AI 解读

The contact rate and associated contact number determine the rate of spread of an infectious disease whose population dynamics are described by a mathematical model. It is shown how to obtain least-squares estimates of the contact rate for a standard homogeneous univariate model and a four-group model with different contact rates between the groups. The results of a small scale simulation are presented in the case of the four-group model. It is argued that the least-squares…