一类零膨胀广义线性模型极大似然估计的相合性与渐近正态性

讨论了响应变量为单参数指数族且在零点处膨胀的广义线性模型的大样本性质，对其参数进行了极大似然估计，给出了一些正则条件.基于所提出的正则条件，证明了模型参数极大似然估计的相合性与渐近正态性.     

Anisotropy Effects and Observational Data on the Constraints of Evolution Dark Energy Models

We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset.     

Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

Empirical Likelihood Inference for Functional Coefficient ARCH-M Model

Empirical likelihood inference for parametric and nonparametric parts in functional coefficient ARCH-M models is investigated in this paper. Firstly, the kernel smoothing technique is used to estimate coefficient function δ(x). In this way we obtain an estimated function with parameter β.Secondly, the empirical likelihood method is developed to estimate the parameter β. An estimated empirical log-likelohood ratio is proved to be asymptotically standard chi-squred, and the maximum empirical likelihood estimation(MELE) for β is shown to be asymptotically normal. Finally, based on the MELE of β, the empirical likelihood approach is again applied to reestimate the nonparametric part δ(x). The empirical log-likelohood ratio for δ(x) is proved to be also asymptotically standard chi-squred. Simulation study shows that the proposed method works better than the normal approximation method in terms of average areas of confidence regions for β, and the empirical likelihood confidence belt for δ(x) performs well.     

Optimal insurance with belief heterogeneity and incentive compatibility

People may evaluate risk differently in the insurance market. Motivated by this, we examine an optimal insurance problem allowing the insured and the insurer to have heterogeneous beliefs about loss distribution. To reduce ex post moral hazard, we follow Huberman et al. (1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the incentive-compatible constraint. Under the assumption that the insurance premium is calculated by the expected value principle, we establish a necessary and sufficient condition for an optimal insurance solution and provide a practical scheme to improve any suboptimal insurance strategy under an arbitrary form of belief heterogeneity. By virtue of this condition, we explore qualitative properties of optimal solutions, and derive optimal insurance contracts explicitly for some interesting forms of belief heterogeneity. As a byproduct of this investigation, we find that Theorem 3.6 of Young (1999) is not completely true.     

累积Logistic回归模型结构变点的序贯检验

分类时间序列在生物医学、社会学和遗传学等领域有着广泛的应用,累积Logistic回归模型是分类时间序列建模的一类重要模型.本文基于偏似然得分过程(Partial likelihood score process)提出一种变点序贯检验方法,监测累积Logistic回归模型的结构是否发生变化.原假设下推导检验统计量的极限分布,备择假设下证明其一致性.模拟试验和实例分析说明了方法的有效性.     

Monomer relative affinity in a copolymer

This paper analyzes data from experiments on simple polymer chains. It measures the extent to which a particular monomer prefers to link with another of the same type. To analyze the data, it derives the likelihood function for a two‐state Markov model in which only the number in each state, but not the order, is observed. This technology is applied to a data set on which experimenters mixed lactic‐glycolic monomers with a known proportion of a contaminant consisting of an extra lactic acid. The resulting copolymers were subjected to matrix‐assisted laser desorption ionization mass spectrometry. This records the number of copolymers at each atomic weight, which can be associated with a given length of copolymer and number of contaminant monomers. Analysis of the data shows that the proportion of contaminant monomers exceeded the proportion of experimentally induced contaminant. Maximum likelihood estimates using the data show that lactic‐glycolic monomers show a positive affinity for the contaminant. Copyright © 2015 John Wiley & Sons, Ltd.     

A Cross-Entropy Approach to the Estimation of Generalized Linear Multilevel Models

In this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online.     

Precision Matrix Estimation With ROPE

It is known that the accuracy of the maximum likelihood-based covariance and precision matrix estimates can be improved by penalized log-likelihood estimation. In this article, we propose a ridge-type operator for the precision matrix estimation, ROPE for short, to maximize a penalized likelihood function where the Frobenius norm is used as the penalty function. We show that there is an explicit closed form representation of a shrinkage estimator for the precision matrix when using a penalized log-likelihood, which is analogous to ridge regression in a regression context. The performance of the proposed method is illustrated by a simulation study and real data applications. Computer code used in the example analyses as well as other supplementary materials for this article are available online.     

Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.