A note on goodness-of-fit test of continuation ratio logistic regression models under case–control data

We extend the discussion of Qin and Zhang's [1997. A goodness of fit test for logistic regression models base on case–control data. Biometrika 84, 609–618] goodness-of-fit test of logistic regression under case–control data to continuation ratio logistic regression (CRLR) models. We first showed that the retrospective CRLR model, which is valid for case–control data (the null hypothesis _H0)${\mathrm{H}}_0)$, is equivalent to an I  -sample semiparametric model. Then under _H0${\mathrm{H}}_0$, we find the semiparametric profile empirical likelihood estimators of distributions of the covariate conditioning on each response category and use them to define a Kolmogorov–Smirnov type test for assessing the global fit of CRLR models under case–control data. Unlike prospective CRLR models, retrospective CRLR models cannot be partitioned to a series of retrospective binary logistic regression models studied by Qin and Zhang [1997. A goodness of fit test for logistic regression models base on case–control data. Biometrika 84, 609–618].     

Generalized Additive Models for Zero‐Inflated Data with Partial Constraints

Abstract. Zero‐inflated data abound in ecological studies as well as in other scientific fields. Non‐parametric regression with zero‐inflated response may be studied via the zero‐inflated generalized additive model (ZIGAM) with a probabilistic mixture distribution of zero and a regular exponential family component. We propose the (partially) constrained ZIGAM, which assumes that some covariates affect the probability of non‐zero‐inflation and the regular exponential family distribution mean proportionally on the link scales. When the assumption obtains, the new approach provides a unified framework for modelling zero‐inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We develop an iterative estimation algorithm, and discuss the confidence interval construction of the estimator. Some asymptotic properties are derived. We also propose a Bayesian model selection criterion for choosing between the unconstrained and constrained ZIGAMs. The new methods are illustrated with both simulated data and a real application in jellyfish abundance data analysis.     

刻画知识与信念的自信逻辑系统

理性认知主体的知识与信念具有可反省性、知识向信念转化等特征。我们可仿造真性模态逻辑的技术方法定义普遍有效式,构造极小正规认知系统ME。该系统具有可靠性和完备性,在此基础上添加一些公理序列可得到许多不同的正规认知逻辑系统。这些系统都从某种意义上刻画了知识与信念,揭示了二者的区别与联系。出于不同的认识论观点,这些系统在公理序列的选择、刻画知识与信念的程度、推理能力等方面存在着一定的差别。     

Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case

We establish consistency and asymptotic normality of the quasi‐maximum likelihood estimator in the linear ARCH model. Contrary to the existing literature, we allow the parameters to be in the region where no stationary version of the process exists. This implies that the estimator is always asymptotically normal.     

M-estimation of the accelerated failure time model under a convex discrepancy function

Based on the Kaplan–Meier weight functions, we introduce a class of M-estimators of regression parameters for the accelerated failure time (AFT) model with right censored data. The proposed M-estimator is root-n consistent and asymptotically normal under appropriate assumptions. For robustness analysis, we also derive the corresponding influence functions. Appropriate criteria are developed for tests of hypotheses concerning regression parameters. The results are applied to several particular cases. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies.     

Likelihood Contour Method for the Calculation of Asymptotic Upper Confidence Limits on the Risk Function for Quantitative Responses

This article develops a computationally and analytically convenient form of the profile likelihood method for obtaining one-sided confidence limits on scalar-valued functions phi = phi(psi) of the parameters psi in a multiparameter statistical model. We refer to this formulation as the likelihood contour method (LCM). In general, the LCM procedure requires iterative solution of a system of nonlinear equations, and good starting values are critical because the equations have at least two solutions corresponding to the upper and lower confidence limits. We replace the LCM equations by the lowest order terms in their asymptotic expansions. The resulting equations can be solved explicitly and have exactly two solutions that are used as starting values for obtaining the respective confidence limits from the LCM equations. This article also addresses the problem of obtaining upper confidence limits for the risk function in a dose-response model in which responses are normally distributed. Because of normality, considerable analytic simplification is possible and solution of the LCM equations reduces to an easy one-dimensional root-finding problem. Simulation is used to study the small-sample coverage of the resulting confidence limits.     

非参数计量经济联立模型的变窗宽估计理论

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用. 文章将非参 数回归模型的局部线性估计方法与传统联立方程模型估计方法相结合,在随机设计(模型中所 有变量为随机变量) 下,提出了非参数计量经济联立模型的局部线性工具变量变窗宽估计并利 用概率论中大数定理和中心极限定理等在内点处研究了它的大样本性质,证明了它的一致性 和渐近正态性,它在内点处的收敛速度达到了非参数函数估计的最优收敛速度     

Estimation du comportement asymptotique des autocovariances et autocorrelations empiriques de processus multivariéeas

Statistics based on the sample autocovariances are widely used in time-series analysis. Estimators of the asymptotic covariance between the sample autocovariances are commonly derived from the so-called Bartlett's formula. However, this formula essentially holds for linear processes. This entails that for a wide range of nonlinear time series the above-mentioned estimators are not suitable. In this paper the behaviour of an alternative estimator is studied within the framework of centered or uncentered multivariate strongly mixing processes. Applications to differential functions of sample autocovariances, such as the sample autocorrelations, are considered.