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具有非平稳相关误差的多元回归模型AI 解读

We consider the estimation of parameters of a multiple regression model with nonstationary errors. We assume the nonstationary errors satisfy a time‐dependent autoregressive process and describe a method for estimating the parameters of the regressors and the time‐dependent autoregressive parameters. The parameters are rescaled as in nonparametric regression to obtain the asymptotic sampling properties of the estimators. The method is illustrated with an example taken from…

利用 Cholesky 分解进行多元谱分析AI 解读

We propose to smooth the Cholesky decomposition of a raw estimate of a multivariate spectrum, allowing different degrees of smoothness for different elements. The final spectral estimate is reconstructed from the smoothed Cholesky elements, and is consistent and positive definite. More importantly, the Cholesky decomposition matrix of the spectrum can be used as a transfer function in generating time series whose spectrum is identical to the given spectrum at the Fourier…

高斯浓度图的模型选择AI 解读

A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e. conditional independences associated with G, which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients. By means of Fisher's z‐transformation and Šidák's correlation inequality, conservative simultaneous confidence intervals for the…

失效原因被遮蔽的竞争风险模型：基于 EM 算法的推断AI 解读

In this paper we propose inference methods based on the EM algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second‐stage data. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause‐specific hazard functions and of the masking probabilities is performed via an EM algorithm. Both the E‐ and M‐steps can be solved in closed form under the full model and under…

多元二元数据交替逻辑回归的置换不变性AI 解读

A practically important but not so obvious result is that alternating logistic regression is invariant to permutations of the response variables within clusters. In this note, we give a short proof of the invariance result using a pairwise likelihood argument. The same proof can be used to establish invariance for a more general class of estimating equations based on conditional residuals. As it stands, the invariance theory is incomplete because existing standard error…

受试者工作特征曲线的非参数置信区间AI 解读

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug‐in rule for bandwidth choice,…

Higher‐order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on θ. A modified likelihood ratio statistic is…

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Kaplan–Meier 估计的代价AI 解读

Miller has studied the asymptotic efficiency of the nonparametric, Kaplan–Meier survival estimator relative to parametric estimates based on the exponential and Weibull distributions. He concluded that in certain cases, the asymptotic efficiency is low and recommended that analysts give more consideration to parametric estimators, particularly for estimation of small tail probabilities. In this article we revisit this issue and examine the performance of the nonparametric…

利用子抽样进行空间各向同性的非参数检验AI 解读

A common requirement for spatial modeling is the development of an appropriate correlation structure. Although the assumption of isotropy is often made for this structure, it is not always appropriate. A conventional practice when checking for isotropy is to informally assess plots of direction-specific sample (semi)variograms. Although a useful diagnostic, these graphical techniques are difficult to assess and open to interpretation. Formal alternatives to graphical…

后验模拟器的正确性检验AI 解读

Analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments. This article develops simple tests of posterior simulators that detect both kinds of errors, and uses them to detect and correct errors in two previously published articles. The tests exploit the fact that a Bayesian model specifies the joint distribution of observables (data) and unobservables (parameters). There are two joint distribution…

纵向数据半参数建模的新估计与模型选择程序AI 解读

Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An…

协变量缺失的非线性混合效应模型：精确与近似推断AI 解读

Nonlinear mixed-effects (NLME) models are popular in many longitudinal studies, including human immunodeficiency virus (HIV) viral dynamics, pharmacokinetic analyses, and studies of growth and decay. In practice, covariates in these studies often contain missing data, and so standard complete-data methods are not directly applicable. In this article we propose Monte Carlo parameter-expanded (PX)-EM algorithms for exact and approximate likelihood inferences for NLME models…

通过似然基追踪进行变量选择与模型构建AI 解读

This article presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log-likelihood into the sum of different functional components such as main effects and interactions, with each component represented by appropriate basis functions. Basis functions are chosen to be compatible with variable selection and model…

一般处理机制下的因果推断AI 解读

In this article we develop the theoretical properties of the propensity function, which is a generalization of the propensity score of Rosenbaum and Rubin. Methods based on the propensity score have long been used for causal inference in observational studies; they are easy to use and can effectively reduce the bias caused by nonrandom treatment assignment. Although treatment regimes need not be binary in practice, the propensity score methods are generally confined to…

不规则时点重复测量中由工作相关模型构造无偏估计方程AI 解读

The method of generalized estimating equations (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation…

经典测量误差线性模型中若干得分检验的不变性AI 解读

The linear model with classical measurement error is an alternative to the standard regression model, in which it is assumed that the independent variables are subject to error. This assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model. However, in some cases, inferences remain unchanged even though the independent variables are assumed to be subject to error. This article…

单位根分位数自回归推断AI 解读

We study statistical inference in quantile autoregression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey–Fuller distribution, but rather a linear combination of the Dickey–Fuller distribution and the standard normal, with the weight determined by the correlation coefficient of related time series.…

模型选择后的统计推断AI 解读

Typical modeling strategies involve model selection, which has a significant effect on inference of estimated parameters. Common practice is to use a selected model ignoring uncertainty introduced by the process of model selection. This could yield overoptimistic inferences, resulting in false discovery. In this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model…

协变量测量误差异质时的生存分析AI 解读

This article is motivated by a time-to-event analysis where the covariate of interest was measured at the wrong time. We show that the problem can be formulated as a special case of survival analysis with heterogeneous covariate measurement error and develop a general analytic framework. We study the asymptotic behavior of the naive partial likelihood estimates and analytically demonstrate that under the heterogeneous measurement error structure and the assumption that all…

时间扭曲随机曲线的函数凸平均与同步AI 解读

Data that can be best described as a sample of curves are now fairly common in science and engineering. When the dynamics of development, growth, or response over time are at issue, subjects or experimental units may experience events at different temporal paces. For functional data where trajectories may be individually time-transformed, it is usually inadequate to use commonly used sample statistics, such as the cross-sectional mean or median or the cross-sectional sample…

广义加性模型中稳定高效的多重平滑参数估计AI 解读

Representation of generalized additive models (GAM's) using penalized regression splines allows GAM's to be employed in a straightforward manner using penalized regression methods. Not only is inference facilitated by this approach, but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross-validation. The current fitting and…

预测误差的估计AI 解读

Having constructed a data-based estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (1) penalty methods such as Cp, Akaike's information criterion, and Stein's unbiased risk estimate that depend on the covariance between data points and their corresponding predictions; and (2) cross-validation and related…

面板模型中未知形式序列相关的小波检验AI 解读

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet-based tests for serial correlation of unknown form in the estimated residuals of a…