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贝叶斯非参数生存分析AI 解读

This article considers a Bayesian nonparametric approach to a (right) censored data problem. Although the results are applicable to a wide variety of such problems, including reliability analysis, the discussion centers on medical survival studies. We extend the posterior distribution of percentiles given by Hill (1968) to obtain predictive posterior probabilities for the survival of one or more new patients, using data from other individuals having the same disease and…

通过广义判别分析构造树形分类规则AI 解读

The problem of constructing classification rules that can be represented as decision trees is considered. Each object to be classified has an associated x vector containing possibly incomplete covariate information. Tree construction is based on the information provided in a “learning sample” of objects with known class identities. The x vectors in the learning sample may have missing values as well. Procedures are proposed for each of the components of classifier…

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小期望格频数频数表使用卡方统计量的警示AI 解读

When applied to frequency tables with small expected cell counts, Pearson chi-squared test statistics may be asymptotically inconsistent even in cases in which a satisfactory chi-squared approximation exists for the distribution under the null hypothesis. This problem is particularly important in cases in which the number of cells is large and the expected cell counts are quite variable. To illustrate this bias of the chi-squared test, this article considers the Pearson…

具有指数条件分布的二元分布AI 解读

It is frequently easier to visualize conditional distributions of experimental variables rather than joint distributions. In this article we consider the most general class of bivariate distributions such that both sets of conditional densities are exponential. The class proves to be remarkably simple to describe: The joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral. The joint…

一类离散分布的参数正交化AI 解读

The standard contagious distributions (see Douglas 1980) have been used in such varied fields as biology and automobile insurance, often to model various physical phenomena as well as provide a good fit to count data when other models are inadequate. Unfortunately, the parameterizations often used when working with these distributions normally lead to extremely high correlations of the maximum likelihood estimators (MLE's). This tends to lead to mathematical complexities,…

用于贝叶斯非参数预测密度的逻辑斯蒂正态分布AI 解读

This article models the common density of an exchangeable sequence of observations by a generalization of the process derived from a logistic transform of a Gaussian process. The support of the logistic normal includes all distributions that are absolutely continuous with respect to the dominating measure of the observations. The logistic-normal family is closed in the prior to posterior Bayes analysis, with the observations entering the posterior distribution through the…

ARMA 参数估计的回归方法AI 解读

Regression procedures for parameter estimation in autoregression moving average (ARMA) models are discussed, mainly for providing initial estimates for iterative maximization of a Gaussian likelihood. An iterative procedure of Spliid (1983) is compared to a procedure of Hannan and Rissanen (1982), and a global convergence result is established for an iterative modification of Spliid's procedure. Spliid's iteration does not always converge; when it does, it has the same…

非参数加速失效时间模型中的线性插值AI 解读

Assuming a nonparametric accelerated failure-time model, a method is proposed for extrapolating low stress-response probabilities on negative-sloping line segments in the stress-failure-time plane. The method (analogous to linear interpolation in dose-response studies) results in simultaneous extrapolation ahead in time and down in stress. In the two-sample (two stress level) setting, a goodness-of-fit test of the nonparametric model is considered and two hypothesis tests…

通过最小化高效尺度构造高崩溃点回归估计AI 解读

A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a new scale estimate, τ, applied to the residuals. Asymptotically, a τ estimate is equivalent to an M estimate with a ψ function given by a weighted average of two ψ functions, one…

排序集样本的刻画及其在分布函数估计中的应用AI 解读

Ranked-set sampling has been shown to provide improved estimators of the mean and variance when actual measurement of the observations is difficult but ranking of the elements in a sample is relatively easy. This result holds even if the ranking is imperfect. In this article, we provide a characterization of a ranked-set sample that makes the source of this additional information intuitively clear. It is applied to show that the empirical distribution function of a…

重症监护病房患者结局的预测AI 解读

Statisticians are being asked with increasing frequency to develop models for occurrences in medical environments. Until recently, only subjective models were available to predict mortality for patients in an intensive care unit (ICU). These models were based on variables and associated weights determined by panels of medical “experts.” This article shows how multiple logistic regression (MLR) can be used to develop an objective model for prediction of hospital mortality…

复发事件分析：随机区间计数数据的非参数方法AI 解读

Many clinical trials require comparison among treatment groups of the rates over time of a particular recurrent event. The event typically reflects disease morbidity rather than mortality. Some examples are episodes of hypoglycemia in diabetics, angina pectoris in patients with heart disease, and seizures in epileptics. Trial protocol often requires that each patient report only the number of events occurring between clinic visits, so the exact times of the successive events…

锥约束对数线性模型中 I 投影与最大似然估计的对偶性AI 解读

Important order restrictions and general log-linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone. Here we exhibit a duality relationship (by way of a Fenchel duality theorem) between these types of problems and projections in I-divergence geometry. We show that many cone-constrained maximum likelihood estimation problems are exactly equivalent to an I…

基于删失数据的 Shapiro–Wilk 指数分布检验AI 解读

In this article we present a modification of the Shapiro-Wilk (1972) exponentiality test when the sample is censored. The test statistic is constructed by using the normalized waiting times based on the sample data, and is shown to have the same null distribution as the uncensored case with a corresponding reduction in sample size. Stephens's (1978) modification of the Shapiro-Wilk statistic for known origin is also modified, to allow censoring in the sample. Again, the test…

指定分位数的拟单峰先验下后验概率的范围AI 解读

Suppose several quantiles of the prior distribution for θ are specified or, equivalently, the prior probabilities of a partitioning collection of intervals {Ii } are given. In addition, suppose that the prior distribution is assumed to be unimodal. Rather than selecting a single prior distribution to perform a Bayesian analysis, it is of interest to consider the class of all prior distributions compatible with these inputs. For this class and unimodal likelihood functions,…

Steel 多处理对照多元符号检验的推广AI 解读

Steel (1959) introduced a nonparametric multivariate sign test to allow one to compare p ≥ 2 test treatments simultaneously with a control or standard treatment in a randomized-block setting. Steel proposed using blocks of size p + 1 composed of one observation from each treatment. Intuitively, it seems that the control should be observed more often that a test treatment, because the control is involved in all treatment-control comparisons and an individual test treatment is…

随机完全区组设计中秩变换程序的渐近相对效率AI 解读

This article provides insight into the powers of alternative tests for experimental effects in the presence of a blocking factor. Three rank tests and the usual F test are compared using asymptotic relative efficiencies (ARE's). Rank tests provide a useful alternative method of analysis when the assumptions of the F test are not met. Further, rank tests are usually more powerful than the F test when outliers are present or when the distribution of the data possesses heavy…

重复测量设计中检测处理效应的非参数方法AI 解读

Sufficient conditions are given that guarantee the limiting distribution of a test proposed by Agresti and Pendergast (1986) to detect treatment effects in repeated-measures designs. The test, which is appropriate for either the original or aligned data, is related to one proposed by Koch (1969) and to the rank-transformation statistic. Using Pitman asymptotic-relative-efficiency comparisons, situations are presented where these tests are more efficient than their standard…