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基于部分信息的一致且稳健的位置参数贝叶斯程序AI 解读

We consider Bayes procedures for a location parameter $\theta$ that are robust with respect to the shape of the distribution $F$ of the data. The case where $F$ is fixed (nonrandom) and the case where $F$ has a Dirichlet distribution are both treated. The procedures are based on the posterior distributions of the location parameter given the partial information contained in a robust estimate of location. We show consistency and asymptotic normality of the procedures and give…

两个总体累积风险的图形比较AI 解读

We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change Δ(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an…

两个总体累积风险的图形比较AI 解读

We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change Δ(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an…

两样本广义优势率模型的估计与检验AI 解读

The generalized odds ratio for a survival variable T is defined as Λ T (t | c) = c -1[1 - Sc (t)]/Sc (t) for c > 0 and -log S(t) for c = 0, where S(t) = Pr(T > t). This ratio coincides with the integrated hazard for c = 0 and the odds ratio for c = 1. When the distribution of T depends on a covariate vector, we assume that conditionally on the covariates, log Λ T (t | c) is linear in the covariates. This model is a generalization of the proportional hazard model (PHM), which…

比例风险模型中中位与平均生存时间的估计及置信区间AI 解读

Estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model. For median survival, the methods apply to censored data. The procedures are based on Cox's partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on Breslow's estimate of the baseline hazard function. The asymptotic properties of these semiparametric estimates are developed and they…

比例风险模型部分似然方法向一般变换模型的扩展AI 解读

Estimates of the linear model parameters in a linear transformation model with unknown increasing transformation are obtained by maximizing a partial likelihood. A resampling scheme (likelihood sampler) is used to compute the maximum partial likelihood estimates. It is shown that for a certain "local" parameter set where the "signal to noise ratio" is small, it is asymptotically possible to estimate the linear model parameters using the partial likelihood as well as if the…

比例风险模型中生存时间中位数与均值的估计及置信区间AI 解读

Estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model. For median survival, the methods apply to censored data. The procedures are based on Cox's partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on Breslow's estimate of the baseline hazard function. The asymptotic properties of these semiparametric estimates are developed and they…

基于变换数据的统计检验AI 解读

The problem of testing hypotheses in linear models when the original data have been transformed is considered. It is assumed that the transformation involves an unknown parameter that has to be estimated from the data. For certain important testing problems it is found that the asymptotic level and power is as if λ had been assumed known. Asymptotic efficiency results show that when the Box-Cox transformation is used, tests based on transformed data have good power…

重新审视数据变换分析AI 解读

Following Box and Cox (1964), we assume that a transform Z i = h(Yi , λ) of our original data {Yi } satisfies a linear model. Consistency properties of the Box-Cox estimates (MLE's) of λ and the parameters in the linear model, as well as the asymptotic variances of these estimates, are considered. We find that in some structured models such as transformed linear regression with small to moderate error variances, the asymptotic variances of the estimates of the parameters in…

(NOTE: Each chapter concludes with Problems and Complements, Notes, and References.) 1. Statistical Models, Goals, and Performance Criteria. Data, Models, Parameters, and Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families. 2. Methods of Estimation. Basic Heuristics of Estimation. Minimum Contrast Estimates and Estimating Equations. Maximum Likelihood in Multiparameter Exponential Families. Algorithmic Issues. 3.…

若干非线性模型中的估计AI 解读

Extensions of linear model contrasts to general and location-scale models are proposed. These extensions are defined in terms of shift functions which measure how much the variables from one population must be shifted to be aligned in distribution with the variables from another. A general estimate based on empirical distribution functions and three estimates appropriate for the location-scale model are considered and compared in terms of asymptotic relative efficiencies. An…

若干非线性模型中的估计AI 解读

Extensions of linear model contrasts to general and location-scale models are proposed. These extensions are defined in terms of shift functions which measure how much the variables from one population must be shifted to be aligned in distribution with the variables from another. A general estimate based on empirical distribution functions and three estimates appropriate for the location-scale model are considered and compared in terms of asymptotic relative efficiencies. An…

对称性的图形诊断与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…

分布对称性的图示与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…