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利用高阶导数参数信息改进非参数曲线估计AI 解读

We suggest a method for using parametric information to modify a nonparametric estimator at the level of relatively high-order derivatives. The technique represents an alternative to methods that first fit a parametric model and then adjust it. In particular, relative to a 'nonparametric estimator with a parametric start', our estimator is not biased by the differences between parametric and nonparametric fits to low-order derivatives, since we effectively remove all the…

采用 CAR(1) 分布的层级模型后验分布AI 解读

We examine properties of the conditional autoregressive model, or CAR(1) model, which is commonly used to represent regional effects in Bayesian analyses of mortality rates. We consider a Bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper. We give sufficient conditions for the…

方差分量模型中的正交性与变换AI 解读

We consider variance components and other models for repeated measures in which a general transformation is applied to the response variable. Using Cox & Reid's (1987) concept of parameter orthogonality and some approximations to the information matrix we show that the intraclass correlation coefficient in the one-way model is robust to the choice of transformation. This robustness result generalises to a vector of parameters determining the correlation structure, to more…

通过近似条件化改进精确检验AI 解读

The often conservative nature, for discrete data, of so-called exact tests seems usually the result of unnecessarily precise conditioning. We consider avoiding this by conditioning only approximately on the sufficient statistics for nuisance parameters. Modest relaxation of conditioning results in small loss in terms of the rationale for conditional inference, but can greatly reduce the difficulties caused by discreteness. Exact calculations of p-values based on approximate…

基于预测方差的回归模型最优设计准则AI 解读

In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed ΙL-optimality, is analogous to Kiefer's Φk-criterion but is based on predicted variance, whereas Kiefer's class is based on the eigenvalues of the information matrix; L-optimal designs are invariant with respect to different parameterisations of the model and contain G- and D- optimality as special cases. We provide a general equivalence…

右删失数据中连续事件间隔时间分布的非参数估计AI 解读

In many follow-up studies, each subject can potentially experience a series of events, which may be repetitions of essentially the same event or may be events of entirely different natures. This paper provides a simple nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow-up time is subject to right censoring. The estimator is consistent and, upon proper normalisation, converges weakly to a zero-mean…

半参数选择偏差模型的最大似然估计及其艾滋病疫苗试验应用AI 解读

The following problem is treated: given s possibly selection biased samples from an unknown distribution function, and assuming that the sampling rule weight functions for each of the samples are mathematically specified up to a common unknown finite-dimensional parameter, how can we use the data to estimate the unknown parameters? We propose a simple maximum partial likelihood method for deriving the semiparametric maximum likelihood estimator. A discussion of assumptions…

摘要暂缺

利用高质量标记信息的超高效风险率估计AI 解读

We show that a nonparametric one-dimensional hazard as a function of time can be estimated √n-consistently if a high-quality marker is observed. Keywords:Counting process; Hazard; Kernel; Marker; Nonparametric estimation; Survival analysis.

杂论：模型误设下病例对照分析与完整队列分析的比较AI 解读

We investigate the question of whether or not estimates of relative risk from matched case-control studies well represent the population from which they were drawn. We derive the formula for the asymptotic maximum partial likelihood estimators from nested case-control studies when the Cox proportional hazards model is misspecified and compare these to the corresponding full cohort values under various types of model misspecification, such as covariate omission, mismodelling…

存在干扰参数时的经验似然AI 解读

Empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood. It is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic, such as the aymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is true in the presence of nuisance parameters. Recent work by Qin & Lawless (1994) indicates that the…

利用单变量分布评估多变量非正态性AI 解读

This paper proposes diagnostics that can indicate regions where multivariate distributions are poorly behaved in the sense that they are far from normal. The measure of nonnormality developed by Slate (1994) for univariate distributions is extended to multivariate parametric models by application to univariate marginal and conditional distributions. The approach is illustrated for univariate conditional distributions using dynamic graphics in Xlisp-Stat (Tierney, 1990).…

评估状态空间过程中的观测预测影响AI 解读

An important inferential objective in state space modelling is to recover unobserved states using fixed-interval smoothing. Thus, the identification of cases which have a substantial influence on the smoothers is a relevant practical problem. To facilitate this identification, we propose a case-deletion diagnostic which can be easily computed using the outputs of the standard filtering and smoothing algorithms. Our diagnostic is defined as the Kullback-Leibler directed…

摘要暂缺

缺失数据非参数分析的递归算法AI 解读

The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this…

缺失数据广义估计方程中的完全随机缺失检验AI 解读

We consider inference from generalised estimating equations when data are incomplete. A test for missing completely at random is proposed to help decide whether or not we should adjust estimating equations to correct the possible bias introduced by a missing-data mechanism that is not missing completely at random. Likelihood ratio tests have been introduced to test the missing completely at random hypothesis (Fuchs, 1982; Little, 1988). For the estimating equation setting,…

组序贯检验后的无偏估计AI 解读

It is shown that, in a group sequential test about the drift θ of a Brownian motion Χ(t) stopped at time Τ, the sufficient statistic (Τ, Χ(Τ)) is not complete for θ. There exist infinitely many unbiased estimators of θ and none has uniformly minimum variance. A truncation-adaptable criterion is proposed, and the uniformly-minimum-variance estimator among all truncation-adaptable unbiased estimators is found. This estimator is identical to estimators of Ferebee (1983) and…

频率估计的快速高效技术：解释与推广AI 解读

In Quinn & Fernandes (1991), an iterative technique was presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is more robust to poor initial estimates than is the periodogram maximiser. A generalisation to the case of multiple sinusoids is presented in this paper, and it is shown that the original estimator may be interpreted as the maximiser of a smoothed version of the periodogram.

多变量纵向计数数据的状态空间模型AI 解读

We propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process. The Poisson counts are assumed to be conditionally independent given the latent process, both over time and across categories. We consider a regression model where time-varying covariates may enter via either the Poisson model or the latent gamma process. Estimation is based on the Kalman smoother, and we consider analysis of residuals from both the…

刻画变点最大似然估计量的分布行为AI 解读

We consider the problem of estimating the unknown changepoint in a sequence of time-ordered observations. Upper and lower bounds are derived for the asymptotic distribution of the maximum likelihood estimator and methods of approximation are suggested. A computationally efficient algorithm is presented for deriving the bounds and approximations for the asymptotic probabilities of the maximum likelihood estimator when the parameters before and after the changepoint are…

利用变系数模型进行模型诊断AI 解读

The paper motivates the use of varying coefficient models for diagnostics in regression models with continuous and factorial covariates. The varying coefficient model, which is restricted only by assumptions concerning the smoothness of the effects, is considered as the alternative to a parametric generalised linear model. Estimation is based on local likelihood smoothing and asymptotic properties of the estimators are derived. For the investigation of the discrepancy…

非参数似然比置信区间AI 解读

We consider construction of two-sided nonparametric confidence intervals in a smooth function model setting. A nonparametric likelihood approach based on Stein's least favourable family is proposed as an alternative to empirical likelihood. The approach enjoys the same asymptotic properties as empirical likelihood, but is analytically and computationally less cumbersome. The simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as…

札记：删失数据的线性变换模型AI 解读

Recently Cheng, Wei & Ying (1995, 1997) proposed a class of estimation procedures for semiparametric linear transformation models with censored observations. When the support of the censoring variable is shorter than that of the failure time, the estimators are asymptotically biased. In this paper, we present a simple modification of Cheng's estimation procedures for the regression parameters. Through extensive numerical studies with practical sample sizes, we find that the…

短札：通过正态近似由条件信息计算信息矩阵AI 解读

This paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters. Philosophically, the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference. Technically, the method makes use of two facts: the information for a one-dimensional parameter…