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用 Gibbs 抽样展示正态数据模型的贝叶斯推断AI 解读

The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models, including variance components, unordered and ordered means, hierarchical growth curves, and missing data in a crossover trial. In all cases the approach is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries.

具有欧几里得结构模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

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估计参数乘积时按变异系数比例分配样本AI 解读

Consider the problem of allocating a fixed total number of observations or a fixed budget to several populations with the goal of minimizing the variance of the product of sample means, where this product of sample means estimates the product of population means. The main application of this problem is to reliability, where the population mean is the Bernoulli success probability that the respective system component will function and the product is the probability that a…

自回归谱估计量的偏差AI 解读

Bias of the least squares estimator of the log of the spectral density of an autoregression attenuates the peaks of the estimator. Under the assumption of an autoregressive generating process of known finite order, we obtain an expression for the order 1/T bias, where T is the sample length of the observed series. This approximation is a sum of several simple functions of the unknown coefficients. When the spectral density has sharp peaks, one of these functions dominates…

自适应簇抽样AI 解读

In many real-world sampling situations, researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting. This article describes sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit. If any of these additional units satisfies the condition, still more units may be…

基于秩的回归方法诊断AI 解读

Residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model. In this article we explore the properties of the residuals from a rank-based fit of the model. We present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank-based fit. We show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model. Furthermore, our…

酸沉降估计的对数正态方法与移动窗口方法AI 解读

The deposition of heightened levels of sulfuric and nitric acid through rainfall in the United States may adversely affect the environment. For example, soils may become toxic to native tree species because of soil acidification. Ecological effects models being built to study these potential problems have a need for regional deposition estimates with associated measures of uncertainty. However, statistical estimation of the deposition process is complicated by a strong…

Cox 模型中的回归样条：肝病协变量效应应用AI 解读

The Cox proportional hazards model restricts the log hazard ratio to be linear in the covariates. A smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function. A survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines, and the resulting log hazard ratio estimates are compared with those from nonparametric methods. We remove the linear restriction on the log…

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序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

通过自助法迭代校正置信区间覆盖率AI 解读

Iterated bootstrap procedures may be used to reduce error in many statistical problems. We discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n −1/2 in one-sided intervals, but of order n −1 in two-sided intervals. Explicit formulas are provided for the dominant term in coverage error after iteration in each case. These results are used to compare…

自回归谱估计量的偏差AI 解读

Bias of the least squares estimator of the log of the spectral density of an autoregression attenuates the peaks of the estimator. Under the assumption of an autoregressive generating process of known finite order, we obtain an expression for the order 1/T bias, where T is the sample length of the observed series. This approximation is a sum of several simple functions of the unknown coefficients. When the spectral density has sharp peaks, one of these functions dominates…

多元回归的 M 估计AI 解读

Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model.These weighted M-estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator.Comparisons for the l lt least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions.An example reanalyzing the Grunfeld investment data using a smooth…

伴随投影寻踪回归AI 解读

Consider a projection pursuit regression model y = g(α + β x) + ε, with an arbitrary monotonic link function g. We assume the link function is unknown; thus we can only estimate the direction of β, that is, the ratios among the components of β, say, β 1/β 2. The direction of β is a useful estimand that measures, say, how many units of x 2 is equivalent to one unit of x 1 in terms of potency in affecting the outcome y. Projection pursuit regression usually solves the equation…

消费者支出调查中的样本加权方法与总量估计AI 解读

The widely used Principal Person method of weighting households in federal government surveys uses external post-Censal information on population to improve survey sample weights by a form of poststratification. While the Principal Person Methodology can be viewed as part of a procedure to adjust for nonresponse and undercoverage, it is not oriented for efficiently incorporating ancillary information or combining information from multiple surveys into survey estimates of…

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具有欧几里得结构的模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

联邦福利质量控制项目中的回归估计AI 解读

States that administer federal family welfare programs review samples of the beneficiaries to guide corrective actions. Federal agencies review subsamples of the state samples to compute overpayment error rates using a regression estimator. These federal estimates make state-to-state comparisons of quality possible and are also used for fiscal sanctions. Such applications of the regression estimator have been widely challenged. We show that the regression estimates and…

状态依赖效用AI 解读

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of what counts as a constant outcome. Although it is sometimes clear what should be considered constant,…