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基于累积卡方统计量最大分量的多重比较程序AI 解读

Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic are discussed. The Markov properties for the successive components of the cumulative chi-squared statistic are proved and applied for obtaining the p- value of the maximal component in each of the one-way and the two-way analysis of variance models and the two-way contingency table. The power of the multiple comparison procedure is compared with those for some well-known…

实验设计稳健性的新视角AI 解读

A common practical experimental philosophy when the underlying response model is unknown is initially to consider a first order model. A total robustness approach requires that the experimenter account for model underspecification due to possible curvature or interactions. It is reasonable that the experimental design possess protection against the selection of an oversimplified model. However, detection of possible underspecification is also important. This paper introduces…

利用代理结果数据与验证样本进行推断AI 解读

In the context of estimating β from the regression model Pβ(Y|X), relating response Y to covariates X, suppose that only a surrogate response S is available for most study subjects. Suppose that for a random subsample of the study cohort, termed the validation sample, the true outcome Y is available in addition to S. We consider maximum likelihood estimation of β from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to…

存在混淆因素时的时变加速失效时间模型估计AI 解读

Cox & Oakes (1984, p. 66) introduced the ‘strong version’ of the accelerated failure time model with time-dependent exposures. We provide conditions under which this model could be used to estimate, from observational data, the causal effect of a time-varying exposure or treatment on time to an event of interest in the presence of time-dependent confounding variables. We propose a class of semiparametric tests and estimators for the model parameters. This class contains an…

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判别问题中bootstrap与交叉验证误判率估计的偏差和变异AI 解读

Simulation studies have shown that bootstrap and cross-validation estimators of aggregate error rate in discrimination problems have different properties, the former having less variability but greater bias. We show by use of a local alternative model that the main differences in bias and variability emerge only when the populations are close. In this context the bootstrap method has less variability but an order of magnitude greater bias than cross-validation.

贝叶斯分析中的适当似然AI 解读

The validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations. To investigate other cases, a second, more intuitive definition of validity is introduced, based on coverage of posterior sets. This notion of validity suggests that the likelihood must be the density of a statistic, not necessarily sufficient, for posterior probability statements to be valid. A convenient numerical method is proposed to…

大量干扰参数下的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

基于参数的渐近方法AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

Siegel 复合周期性检验统计量的渐近分位点AI 解读

Fisher's test for a periodicity at a single Fourier frequency is often inadequate in practice where it is necessary to test for compound periodicities, i.e. spectral lines at several frequencies. Siegel (1980) derived a test statistic for compound periodicity and provided percentage points for m not exceeding 50, where N = 2m + 1 is the length of the time series. Here the distribution of the test statistic is rewritten to enable computation of exact percentage points for m…

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参数非线性函数后验密度的拉普拉斯展开AI 解读

An asymptotic expansion for marginal posterior densities of nonlinear functions of parameters is derived. The density in question is proportional to an integral over a lower dimensional manifold with the integrand including an appropriate change-in-volume term, Laplace's method is applied to obtain the expansion. Avoiding the difficult step of the explicit parameterization of the manifold, we carry out the expansion via an implicit and local parameterization, and the…

具有自回归移动平均误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

关于回归估计量方差估计的一则说明AI 解读

Särndal, Swensson & Wretman (1989) and Kott (1990a) have proposed two separate estimators for the variance of the regression estimator of a finite population mean based on a simple random sample without replacement. It is shown here that the former approximates for large samples and the latter equals respectively two known variance estimators, relative merits of which are already studied in the literature.

品种对比的信息矩阵与精度矩阵AI 解读

An equational relationship is established between the precision matrix of the estimates of the elementary varietal contrasts and the coefficient matrix of the reduced normal equations for varietal effects in the additive model with blocking in several directions.

基于线性回归模型预测生存概率AI 解读

After fitting survival data with a linear regression model, it is important to know how to use the results to make prediction of the t-year survival probability or median failure time for future patients with certain covariates. We propose some simple prediction procedures without using complicated and unstable nonparametric functional estimates. The new methods are illustrated with the Stanford heart transplant data.

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有限马尔可夫链的经验贝叶斯估计量AI 解读

Using results of Anderson & Goodman (1957), we develop empirical Bayes estimates for the transition probabilities of a finite stationary Markov chain. Some asymptotic properties of these estimators are also derived.

非贝叶斯分类规则的错误率与 Fisher 线性判别的稳健性AI 解读

We call a classification procedure non-Bayes if it does not converge to the Bayes classification procedure. An asymptotic expansion is found for the expected error rate of such a classification rule. This is used to compare the estimates of Fisher's linear discriminant rule, F, and the quadratic discriminant rule, Q, under departures from the equal variance matrices assumption. It is found that F is quite robust to departures from the equal variances assumption.