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处理组与对照组曲线估计的信号提取方法AI 解读

Suppose that the response of a group of subjects, which we call the control group, is monitored over time. At a given time after the start of the experiment, the experimenter intervenes and applies a treatment to a subset of the group. We propose a signal extraction approach to the simultaneous estimation of the treatment and control mean response curves, and their rates of change, imposing a smooth transition constraint between the two curves at the time of intervention. By…

具有相关自相关随机效应的混合模型系统的经验贝叶斯分析AI 解读

Empirical Bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects. Emphasis is placed on the estimation of the random effects and exploration of the relationships between them. Application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors, or “daily…

使用 Jeffreys 先验的广义线性模型贝叶斯分析AI 解读

Generalized linear models (GLM's) have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates. Bayesian analysis of such data requires specification of a prior for the regression parameters in the model used. Uniform priors are very commonly used as conventional noninformative priors. We show, however, that uniform priors for GLM's can lead to improper posterior distributions thus making them undesirable.…

给定先验边际分布时的贝叶斯推断AI 解读

We show how to find bounds on posterior expectations of arbitrary functions of the parameters when the prior marginals are specified but when the complete joint prior is unspecified. We also give a theorem that is useful for finding posterior bounds in a wide range of Bayesian robustness problems. We apply these techniques to two examples. The first example involves a recent clinical trial for extracorporeal membrane oxygenation (ECMO). Our analysis may be regarded as a…

贝叶斯研究者如何预期彼此的信念AI 解读

Our goal is to study general properties of one Bayesian's subjective beliefs about the behavior of another Bayesian's subjective beliefs. We consider two Bayesians, A and B, who have different subjective distributions for a parameter θ, and study Bayesian A's expectation of Bayesian B's posterior distribution for θ given some data Y. We show that when θ can take only two values, Bayesian A always expects Bayesian B's posterior distribution to lie between the prior…

利用 EM 获得渐近方差协方差矩阵：SEM 算法AI 解读

The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic…

市场模型中贝塔系数的时间序列性质检验AI 解读

Understanding the stochastic behavior of beta is fundamental to portfolio risk management. We evaluate the time series properties of beta for oil industry stocks, machinery industry stocks, and a random sample of 100 stocks. Daily returns for stocks in each of these industries and the random sample are obtained from the Center for Research in Security Prices tapes for the period July 1962 through December 1986 and are grouped into 98 quarter-year, and also 49 half-year,…

利用傅里叶级数检验含干扰参数的分布假设AI 解读

We develop a class of smoothed χ 2 tests of distributional hypotheses based on Fourier coefficients used in the density estimation procedure of Fellner. Starting with the simple test of Fx = G, where G is a completely specified hypothesized continuous distribution, we develop tests of the composite null hypothesis Fx − Gα for some vector of unknown parameters α. Variances used in computing the tests vary according to the choice of distributional family and depend on…

置换检验功效蒙特卡洛模拟中的计算投入分配AI 解读

Consider a randomization test in which an observed statistic is compared to a null distribution constructed by first drawing a random sample from the set of all possible permutations of the data and then calculating the statistic anew for each member of the random sample. If the power of such a test is investigated by simulation, the computer code must have two main loops. In the outer loop, which has O iterations, data are generated under a specific alternative hypothesis.…

位置参数的折中最大似然估计量AI 解读

This article describes a new approach for constructing robust location estimators. These estimators are constructed to be nearly optimal in small sample sizes simultaneously for two or more possible underlying shapes of the density of the data. The estimators are weighted averages of the maximum likelihood estimators for the densities considered, where the weights depend on the sample through the likelihood functions. Because of this relationship to the usual MLE's, these…

状态空间模型的自助法：高斯最大似然估计与卡尔曼滤波AI 解读

The bootstrap is proposed as a method for assessing the precision of Gaussian maximum likelihood estimates of the parameters of linear state-space models. Our results also apply to autoregressive moving average models, since they are a special case of state-space models. It is shown that for a time-invariant, stable system, the bootstrap applied to the innovations yields asymptotically consistent standard errors. To investigate the performance of the bootstrap for finite…

多元总体选择的贝叶斯与极小极大样本可容许程序AI 解读

Let P be a class of independent populations each having an underlying multivariate normal distribution with unknown mean vector. Independent vector samples of common size n are drawn from each population in P. We say that a subset G of P is δ*-Pareto-optimal (in P) if no other population in P has the property that each component of its mean vector is larger by at least δ* ≥ 0 than the corresponding component of the mean vector of any given population in G. This article…

合并无偏与可能有偏估计量的 James–Stein 型方法AI 解读

We present a method for combining unbiased sample data with possibly biased auxiliary information. The estimator we derive is similar in spirit to the James–Stein estimator. We prove that the estimator dominates the sample mean under quadratic loss. When the auxiliary information is unbiased, our estimator has risk slightly greater than the usual combined estimator. As the bias increases, however, the risk of the usual estimator is unbounded, while the risk of our estimator…

单参数情形下最大似然估计与后验均值的比较AI 解读

Consider estimation of a scalar parameter θ of a distribution on the basis of a random sample of size n. Possible estimators include the maximum likelihood estimator, n , and the posterior mean with respect to some prior distribution, n . In this article n and n are compared by considering a large-sample version of the Pitman nearness criterion; conditions are given under which n is preferable to n in this sense. Several examples are provided that show that comparisons of n…

数据库错误检测与预测AI 解读

We develop and analyze models for a class of problems involving inferences about uncertain numbers of errors in data bases. In particular, we study two error detection methods. In the duplicate performance method, all items in a data base are processed by two individuals (or machines), and the resulting records are compared to find disagreements, which are then resolved. In the known errors method, a data base is first extended to include additional items known to be in…

有限总体抽样区间估计的无信息贝叶斯方法AI 解读

A noninformative Bayesian approach to interval estimation in finite population sampling is discussed. Given the sample, this method introduces the Polya distribution as a pseudo posterior distribution over the unobserved members of the population. In many cases this distribution yields interval estimates similar to those of standard frequentist theory. In addition, it can be used in situations where the standard methods are difficult to apply, for example, in producing an…

确定性函数的贝叶斯预测及计算机试验设计AI 解读

This article is concerned with prediction of a function y(t) over a (multidimensional) domain T, given the function values at a set of “sites” {t (1), t (2), …, t (n)} in T, and with the design, that is, with the selection of those sites. The motivating application is the design and analysis of computer experiments, where t determines the input to a computer model of a physical or behavioral system, and y(t) is a response that is part of the output or is calculated from it.…

混沌系统的似然与贝叶斯预测AI 解读

There has recently been considerable interest in both applied disciplines and in mathematics, as well as in the popular science literature, in the areas of nonlinear dynamical systems and chaotic processes. By a nonlinear, deterministic dynamical system, we mean a time series in which, starting at some initial condition, the values of the series are some fixed, nonlinear function of the previous states. One of the more intriguing aspects of these models is their propensity…

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潜在真实时间序列及其指标：一种替代方法AI 解读

de Leeuw and McKelvey proposed a method for using two imperfect indicators to predict the values of an unobserved series. In this article we suggest an alternative method that uses the multiple indicator approach to model the true time series and its indicators. We examine the identification status of the model, estimate the parameters by maximum likelihood, and use the Kalman filter to obtain predictions of the unobserved series. The method is applied to the U.S. gross…

利用多元自适应回归样条进行非线性时间序列建模AI 解读

Multivariate Adaptive Regression Splines (MARS) is a new methodology, due to Friedman, for nonlinear regression modeling. MARS can be conceptualized as a generalization of recursive partitioning that uses spline fitting in lieu of other simple fitting functions. Given a set of predictor variables, MARS fits a model in the form of an expansion in product spline basis functions of predictors chosen during a forward and backward recursive partitioning strategy. MARS produces…

广义线性模型导论AI 解读

Part 1 Background scope notation distributions derived from normal distribution. Part 2 Model fitting: plant growth sample birthweight sample notation for linear models exercises. Part 3 Exponential family of distributions and generalized linear models: exponential family of distributions generalized linear models. Part 4 Estimation: method of maximum likelihood method of least squares estimation for generalized linear models example of simple linear regression for Poisson…

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