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利用替代结局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…

存在混杂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…

左截断与右删失数据的风险率估计量比较AI 解读

Left truncation and right censoring arise frequently in practice for life data. This paper is concerned with the estimation of the hazard rate function for such data. Two types of nonparametric estimators based on kernel smoothing methods are considered. The first one is obtained by convolving a kernel with a cumulative hazard estimator. The second one is in the form of a ratio of two statistics. Local properties including consistency, asymptotic normality and mean squared…

快速且准确的近似双重自助法置信区间AI 解读

We propose two new methods for the construction of approximate iterated bootstrap confidence intervals. Our methods follow a saddlepoint approach, but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique. The main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small- to moderately-sized samples and that they achieve this accuracy with very…

贝叶斯分析中适当的似然函数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…

非线性时间序列建模中残差自相关的渐近标准误AI 解读

The asymptotic distribution of residual autocorrelations for some very general nonlinear time series models is derived. This includes the important class of threshold models. Consequently more accurate standard errors for residual autocorrelations can be obtained facilitating model diagnostic checkings in many situations. A small simulation result applying the methodology to threshold models is reported.

一阶非循环自回归中的尾概率近似AI 解读

A saddlepoint expansion is derived for the cumulative distribution function of the least squares estimator of the autoregressive coefficient. The new method is shown to be superior both analytically and numerically to many existing approximations. Unlike other methods the new approximation performs uniformly well over the whole range of the distribution including the extreme tail, even when the sample size is as small as 10.

平均剩余寿命的一种新检验AI 解读

The mean residual life at age t is the expected value of the remaining life beyond that age. A new U-statistic is derived for testing constant versus decreasing mean residual life. The new test is easier to compute and performs better for several alternatives than previous tests.

家庭数据分析的一则说明AI 解读

Because families have varying numbers of offspring, the maximum likelihood estimators of the interclass, or parent-offspring, and intraclass, or offspring-offspring, correlations are difficult to compute (Srivastava, 1984). For this reason, alternative estimators have been proposed, which are not necessarily asymptotically efficient. However, maximum likelihood estimators of the inter- and intraclass correlations in families of constant size can be obtained in closed form,…

参数非线性函数后验密度的拉普拉斯展开AI 解读

SUMMARY 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 ARMA 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…

含时变协变量的加速失效时间模型的半参数估计AI 解读

A class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates. A class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored. These estimates are shown to be consistent, and asymptotically normal with variances that can be consistently estimated. It is also shown that estimators within this class…

判别问题中 bootstrap 与交叉验证误差率估计的偏差和变异性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.

存在大量干扰参数时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…

柯西模型中的条件推断AI 解读

Many computations associated with the two-parameter Cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane. With this convention we show that the family is closed under Mö bius transformation of the sample space: there is a similar induced transformation on the parameter space. The chief raison d'être of the paper, however, is that the two-parameter Cauchy model provides an example of a nonunique…

指数族中更准确的置信区间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…

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…

半参数模型的投影似然函数AI 解读

In a sequence of papers, McLeish (1984), Hutton & Nelson (1986) and Godambe & Heyde (1987) have motivated the use of the quasi-score function as an estimating function for semiparametric models by showing that it is the projection of the true score into a class of unbiased estimating functions. Thus the quasi-score approximates the score within this class of functions. In this paper, we introduce a class of inference functions for independent observations that contain…

Reinsch 与 Speckman 样条的比较AI 解读

In the context of nonparametric regression, spline smoothers can be used both for the estimation of the curve itself and for the estimation of the error variance. We compare two approaches that have been suggested: the Reinsch spline, i.e. roughness penalty, and the Speckman spline, minimax. The comparison is made on the basis of the summed mean squared error for curve estimation and on the basis of a closely related criterion for variance estimation. We show in both…

位置参数估计中的条件稳健性AI 解读

Let Y1,…, Yn denote independent real-valued observations, each distributed according to a density p(y − θ ), where θ is an unknown parameter and p is a symmetric density function. This paper considers robust point estimation of θ from the point of view of conditional inference. Specific measures of the conditional robustness of a location estimator are introduced, as well as measures of the conditional robustness of a particular sample. Location-scale models are also…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

评估后验影响的图形化个案统计量AI 解读

A single number summary of the influence of an observation on the posterior of the parameter of interest is useful, but does not convey all aspects of the effect of deleting the observation. We propose a plot that does convey all the effects of an observation on the posterior.

点过程统计分析的动态方法AI 解读

An approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented. Bayesian inference for processes with explanatory variables is derived in terms of on-line estimation, filtering and prediction. Limiting equations for the time-continuous intensity rate are obtained and solved for the no-covariates case. Examples are provided and the approach is applied in a numerical example.

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.