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A note on the sensitivity to assumptions of a generalized linear mixed model

广义线性混合模型对假设敏感性的一个注记

A simple case of Poisson regression is used to study the potential gain in efficiency from using a mixed model representation. Possible systematic errors arising from misspecification of the random terms in the model are examined. It is shown in particular that for a special but realistic problem, appreciable bias may arise from misspecification of a random component.

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A semiparametric random effects model for multivariate competing risks data

多变量竞争风险数据的半参数随机效应模型

We propose a semiparametric random effects model for multivariate competing risks data when the failures of a particular type are of interest. Under this model, the marginal cumulative incidence functions follow a generalized semiparametric additive model. The associations between the cause-specific failure times can be studied through dependence parameters of copula functions that are allowed to depend on cluster-level covariates. A cross-odds ratio-type measure is proposed…

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Incorporating prior probabilities into high-dimensional classifiers

在高维分类器中纳入类别先验概率

In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of high-dimensional classifiers, partly because there are no likelihoods to be constructed or Bayes risks to be estimated. Nevertheless, including information about prior probabilities…

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On Bayesian testimation and its application to wavelet thresholding

贝叶斯检验与估计及其在小波阈值化中的应用

We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various sparse lp-balls are extended to more general cases. We show that, for a properly chosen prior on the number of nonzero entries of…

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Global and local spectral-based tests for periodicities

检验周期性的全局与局部谱方法

We investigate tests for periodicity based on a spectral analysis of a time series, differentiating between global and local spectral-based tests. Global tests use information across the entire frequency band,whereas local tests are based on a window around the test frequency.We show that many spectral-based tests can be expressed in terms of a regression-based F test, which allows for approximate size and power calculations. Since global tests are usually derived assuming…

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Cross-covariance functions for multivariate random fields based on latent dimensions

基于潜在维度的多变量随机场交叉协方差函数

The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance…

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Sharp bounds on causal effects in case-control and cohort studies

病例对照与队列研究中因果效应的锐界

Evaluating the causal effect of an exposure on a response from case-control and cohort studies is a major concern in epidemiological and medical research. Since causal effects are in general nonidentifiable from such studies, this paper derives bounds on two causal measures: the causal risk difference and the causal risk ratio. We use the potential response approach and a linear programming method to derive sharp bounds on the causal risk difference, and a novel fractional…

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Estimation of the retransformed conditional mean in health care cost studies

医疗费用研究中反变换条件均值的估计

We propose a new approach for analyzing skewed and heteroscedastic health care cost data through regression of the conditional quantiles of the transformed cost. Using the appealing equivariance property of quantiles to monotone transformations, we propose a distribution-free estimator of the conditional mean cost on the original scale. The proposed method is extended to a two-part heteroscedastic model to account for zero costs commonly seen in health care cost studies.…

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Forecasting for quantile self-exciting threshold autoregressive time series models

分位数自激门限自回归时间序列模型的预测

Self-exciting threshold autoregressive time series models have been used extensively, and the conditional mean obtained from these models can be used to predict the future value of a random variable. In this paper we consider quantile forecasts of a time series based on the quantile self-exciting threshold autoregressive time series models proposed by Cai and Stander (2008) and present a new forecasting method for them. Simulation studies and application to real time series…

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On the use of stochastic ordering to test for trend with clustered binary data

利用随机序检验聚类二元数据的趋势

We introduce the use of stochastic ordering for defining treatment-related trend in clustered exchangeable binary data for both when cluster sizes are fixed and when they vary randomly. In the latter case, there is a well-documented tendency for such data to be sparse, a problem we address by making an assumption of interpretability or, equivalently, marginal compatibility. Our procedures are based on a representation of the joint distribution of binary exchangeable random…

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Marginal analyses of longitudinal data with an informative pattern of observations

观测模式具有信息性时的纵向数据边际分析

We consider solutions to generalized estimating equations with singular working correlation matrices, of which the estimator of Diggle et al. (2007) is a special case. We give explicit conditions for consistent estimation when the pattern of observations may be informative. In such cases, simulations reveal reduced bias and reduced mean squared error compared with existing alternatives. A study of peritoneal dialysis is used to illustrate the methodology.

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Functional quadratic regression

函数型二次回归

We extend the common linear functional regression model to the case where the dependency of a scalar response on a functional predictor is of polynomial rather than linear nature. Focusing on the quadratic case, we demonstrate the usefulness of the polynomial functional regression model, which encompasses linear functional regression as a special case. Our approach works under mild conditions for the case of densely spaced observations and also can be extended to the…

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Pseudo-score confidence intervals for parameters in discrete statistical models

离散统计模型参数的伪得分置信区间

We propose pseudo-score confidence intervals for parameters in models for discrete data. The confidence interval is obtained by inverting a test that uses a Pearson chi-squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values. For multinomial models, the pseudo-score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to…

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Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes

向量自回归过程的加权最小二乘近似限制似然估计

We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and…

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Systematic sampling with errors in sample locations

抽样位置存在误差时的系统抽样

Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on…

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Nonparametric Bayesian inference for the spectral density function of a random field

随机场谱密度函数的非参数贝叶斯推断

A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling…

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On doubly robust estimation in a semiparametric odds ratio model

半参数优势比模型中的双重稳健估计

We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models…

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Stochastic approximation with virtual observations for dose-finding on discrete levels

利用虚拟观测在离散剂量水平上进行随机逼近寻量

Phase I clinical studies are experiments in which a new drug is administered to humans to determine the maximum dose that causes toxicity with a target probability. Phase I dose-finding is often formulated as a quantile estimation problem. For studies with a biological endpoint, it is common to define toxicity by dichotomizing the continuous biomarker expression. In this article, we propose a novel variant of the Robbins-Monro stochastic approximation that utilizes the…

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Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach

右删失长度偏倚数据的非参数估计:伪偏似然方法

To estimate the lifetime distribution of right-censored length-biased data, we propose a pseudo-partial likelihood approach that allows us to derive two nonparametric estimators. With its closed-form estimators and explicit limiting variances, this approach retains the simplicity of conditional analysis, and has only a small efficiency loss compared with the unconditional analysis. Under some regularity conditions, we show that the two estimators are uniformly consistent and…

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Tests and confidence intervals for secondary endpoints in sequential clinical trials

序贯临床试验中次要终点的检验与置信区间

In a sequential clinical trial whose stopping rule depends on the primary endpoint, inference on secondary endpoints is an important long-standing problem. Ignoring the possibility of early stopping based on the primary endpoint may result in substantial bias. To address this problem, a commonly used approach is to develop bias correction by estimating the bias in the case of bivariate normal outcomes and appealing to joint asymptotic normality of the statistics associated…

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'Generalized method of moments estimation for linear regression with clustered failure time data'

聚类失效时间线性回归的广义矩估计:引文更正

Although Qu et al. (2000) was cited in § 1 of our paper, it should also have been mentioned as the source of the basis representation of the inverse correlation matrix following our equation (3). Moreover our Theorem 3 rests on arguments similar to those leading to Theorem 1 of Qu et al. (2000). We thank Dr Qu for pointing this out. ‘A group bridge approach for variable selection’ BY JIAN HUANG, SHUANGGE MA, HUILIANG XIE AND CUN-HUI ZHANG [email protected][email…

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A note on automatic variable selection using smooth-threshold estimating equations

利用平滑阈值估计方程自动选择变量

This paper develops smooth-threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero. The resulting estimator enjoys the oracle property in the sense of Fan & Li (2001), even in estimators for which the covariance assumption of Wang & Leng (2007) is violated, such as the Buckley--James estimator. Furthermore, the estimator can be obtained without solving a convex optimization problem. A bic -type criterion for tuning…

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Marginal hazards model for case-cohort studies with multiple disease outcomes

多疾病结局病例队列研究的边际风险率模型

Case-cohort study designs are widely used to reduce the cost of large cohort studies while achieving the same goals, especially when the disease rate is low. A key advantage of the case-cohort study design is its capacity to use the same subcohort for several diseases or for several subtypes of disease. In order to compare the effect of a risk factor on different types of diseases, times to different events need to be modelled simultaneously. Valid statistical methods that…

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A new look at time series of counts

计数时间序列的新视角

This paper proposes a simple new model for stationary time series of integer counts. Previous work has focused on thinning methods and classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric or any other discrete marginal distribution can be readily…

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