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利用鞍点近似构造小样本半数致死剂量置信区间AI 解读

Confidence intervals for the median lethal dose (LD50) and other dose percentiles in logistic regression models are developed using a generalization of the Fieller theorem for exponential families and saddlepoint approximations. Simulation results show that, in terms of one-tailed and two-tailed coverage, the proposed methodology generally outperforms competing confidence intervals obtained from the classical Fieller, likelihood ratio, and score methods. In terms of…

利用鞍点近似对随机系统生存时间进行自助推断AI 解读

Summary The single bootstrap is implemented by using a saddlepoint approximation to determine estimates for the survival and hazard functions of first-passage times in complicated semi-Markov processes. The double bootstrap is also implemented by resampling saddlepoint inversions and provides BCa confidence bands for these functions. Confidence intervals for the mean and variance of first-passage times are easily computed. A new characterization of the asymptotic hazard rate…

多元累积分布函数的鞍点近似及其抽样与离群检验应用AI 解读

Four multivariate distributions commonly arise in sampling theory: the multinomial, multivariate hypergeometric, Dirichlet, and multivariate Pólya distributions. Second-order saddlepoint approximations are given for approximating these multivariate cumulative distribution functions (cdf's) in their most general settings. Probabilities of rectangular regions associated with these cdf's are also approximated directly using second-order saddlepoint methods. All the…

多元累积分布函数的鞍点近似及其在抽样理论与异常值检验中的概率计算AI 解读

Four multivariate distributions commonly arise in sampling theory: the multinomial, multivariate hypergeometric, Dirichlet, and multivariate Pólya distributions. Second-order saddlepoint approximations are given for approximating these multivariate cumulative distribution functions (cdf's) in their most general settings. Probabilities of rectangular regions associated with these cdf's are also approximated directly using second-order saddlepoint methods. All the…

用于生存分析的随机网络模型AI 解读

We present methodology giving highly accurate approximations for Bayesian predictive densities and distribution functions of first passage times between states of a semi-Markov process with a finite number of states. When the states describe a degenerative disorder with an absorbing end state, such predictive distributions are the survival distributions of a patient. We illustrate these methods with a variety of examples, including data from the San Francisco AIDS study. We…

有限总体的 Bootstrap 方法AI 解读

We show that the familiar bootstrap plug-in rule of Efron has a natural analog in finite population settings. In our method a characteristic of the population is estimated by the average value of the characteristic over a class of empirical populations constructed from the sample. Our method extends that of Gross to situations in which the stratum sizes are not integer multiples of their respective sample sizes. Moreover, we show that our method can be used to generate…

块独立性、球形性及方差协方差相等检验的鞍点近似AI 解读

SUMMARY Approximations for the null distribution of various test statistics arising in multivariate analysis using Skovgaard's saddlepoint formula are discussed. In each case an approximation is found with such accuracy as to obviate the need for exact computation.

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多元分析中 Bartlett–Nanda–Pillai 迹统计量的鞍点近似AI 解读

The null distribution of the Bartlett-Nanda-Pillai trace statistic is shown to be equivalent to the conditional distribution of canonical sufficient statistics in a multiparameter exponential family setting. As such, sequential and double saddlepoint approximations are used to approximate the distribution. The existence of tabulated percentiles for the distribution allows for comparison of the accuracy of the various saddlepoint approximations. The ability of the…

预测似然推断及其应用AI 解读

SUMMARY Conditional and marginal predictive likelihood are defined and used in predicting unobserved or missing data. A distinction is made between predictive and estimative goals of a data analysis. Such methodology and distinctions are illustrated in the context of outlier theory and mixed model ANOVA.

回归中一步变量选择的最优性质AI 解读

We consider the selection of the best subset of independent variables of a fixed size for possible inclusion in a regression model. The classical procedures (largest $\mathbb{R}^2$ to enter) are shown to be uniformly invariant Bayes in the sense of Paulson (1952) and Kudo (1956).

基于 Grubbs 型异常值规则修剪数据的非参数区间与点预测AI 解读

For a fixed probability $0 < \gamma < 1$, the "most outlying" $100(1 - \gamma){\tt\%}$ subset of the data from a location model may be located with a Grubbs outlier subset test statistic. This subset is essentially located in terms of its complement, which is the connected $100\gamma{\tt\%}$ span of the data which supports the smallest sample variance. We show that this range of the data may be characterized approximately as the $100\gamma{\tt\%}$ span such that its midpoint…

We demonstrate the admissible Bayes character of two residual error criteria for subset selection of independent variables in normal multivariate regression models. In particular, suppose a linear model includes the independent variable list $X$, and suppose all additional independent variable subsets of size $s$ (fixed) from list $Z$ are under consideration for inclusion in the model. Let $\mathbf{\Sigma}$ be the regression error covariance matrix and $\hat{\mathbf{\Sigma}}(\hat{\mathbf{\Sigma}}_\mathscr{J})$…