Progressive stress accelerated life tests under finite mixture models

In this paper, progressive stress accelerated life tests are considered when the lifetime of a product under use condition follows a finite mixture of distributions. The experiment is performed when each of the components in the mixture follows a general class of distributions which includes, among others, the Weibull, compound Weibull, power function, Gompertz and compound Gompertz distributions. It is assumed that the scale parameter of each component satisfies the inverse power low, the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the parameters under consideration are obtained. A special attention is paid to a mixture of two Rayleigh components. Simulation results are carried out to study the precision of the MLEs and to obtain confidence intervals for the parameters involved.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 1

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

DSGE pileups

The sampling distribution of estimators for DSGE structural parameters tends to be non-normal and/or pile up on the boundary of the theoretically admissible parameter space. This calls into question both the reliability of asymptotic approximations and the presumption of correct specification. This paper seeks to develop a conceptual framework for understanding how these phenomena arise, and to provide pragmatic methods for dealing with them in practice. The results are presented in three examples and a medium scale DSGE model.     

ON THE FIRST–ORDER EFFICIENCY AND ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS OBTAINED FROM DEPENDENT OBSERVATIONS

Abstract. In this paper we study the first–order efficiency and asymptotic normality of the maximum likelihood estimator obtained from dependent observations. Our conditions are weaker than usual, in that we do not require convergences in probability to be uniform or third–order derivatives to exist.
The paper builds on Witting and Nolle's result concerning the asymptotic normality of the maximum likelihood estimator obtained from independent and identically distributed observations, and on a martingale theorem by McLeish.     

THE BIVARIATE EXPONENTIAL DISTRIBUTION; A REVIEW AND SOME NEW RESULTS

Various models have been proposed as bivariate forms of the exponential distribution. A brief but comprehensive review is presented which classifies, interrelates and contrasts the different models and outlines what is known about distributional properties, applicability and estimation and testing of parameters (particularly the association parameter). Some new results are presented for one particular model. Maximum likelihood, and moment–type, estimators of the association parameter are examined. Asymptotic variances are derived and attention is given to the relative efficiency of the estimators and to problems of their evaluation.     

ML– and semiparametric estimation in logistic models with incomplete covariate data

ML–estimation of regression parameters with incomplete covariate information usually requires a distributional assumption regarding the concerned covariates that implies a source of misspecification. Semiparametric procedures avoid such assumptions at the expense of efficiency. In this paper a simulation study with small sample size is carried out to get an idea of the performance of the ML–estimator under misspecification and to compare it with the semiparametric procedures when the former is based on a correct assumption. The results show that there is only a little gain by correct parametric assumptions, which does not justify the possibly large bias when the assumptions are not met. Additionally, a simple modification of the complete case estimator appears to be nearly semiparametric efficient.     

普通似然及经验似然情况下的结点问题

本文在普通似然及经验似然情况下,分别对数据无结点和有结点的情况做了计算,得出在普通似然及经验似然问题中,有结点与无结点情况完全相同的结论。     

Varying Coefficient Regression Models: A Review and New Developments

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.