Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

Variance (Non) Causality in Multivariate GARCH

This paper extends the current literature on the variance-causality topic providing the coefficient restrictions ensuring variance noncausality within multivariate GARCH models with in-mean effects. Furthermore, this paper presents a new multivariate model, the exponential causality GARCH. By the introduction of a multiplicative causality impact function, the variance causality effects becomes directly interpretable and can therefore be used to detect both the existence of causality and its direction; notably, the proposed model allows for increasing and decreasing variance effects. An empirical application evidences negative causality effects between returns and volume of an Italian stock market index future contract.     

Multivariate outlier detection in incomplete survey data: the epidemic algorithm and transformed rank correlations

Summary.  As a part of the EUREDIT project new methods to detect multivariate outliers in incomplete survey data have been developed. These methods are the first to work with sampling weights and to be able to cope with missing values. Two of these methods are presented here. The epidemic algorithm simulates the propagation of a disease through a population and uses extreme infection times to find outlying observations. Transformed rank correlations are robust estimates of the centre and the scatter of the data. They use a geometric transformation that is based on the rank correlation matrix. The estimates are used to define a Mahalanobis distance that reveals outliers. The two methods are applied to a small data set and to one of the evaluation data sets of the EUREDIT project.     

黑龙江省工业资本产出贡献率的实证分析

提高老工业基地的经济增长水平,是一个意义深远的课题。黑龙江省老工业基地发展相对落后的原因在于工业实收资本结构的不合理,国家资本偏高,个人资本绝对性偏低,单位个人资本效率是单位国家资本的五倍。法人资本的多层代理也是造成黑龙江省工业发展相对落后的原因之一。对此,应妥善解决委托代理失灵问题,大力促进民营资本的发展,加快国有经济布局的战略性调整。     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

我国货币政策失效的原因分析及对策

1997年以来,我国的货币政策在经济增长中起到了一定的作用,但也存在一些失效,主要表现在利率机制、准备金政策、公开市场业务等方面存在缺陷。因此,必须不断完善我国的货币政策,以便更好地为经济增长提供政策指导。     

On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

间歇开放系统的可靠性分析与数值计算

研究了一种新型的可靠性系统，即间歇开放系统。在建立数学模型的基础上，我们详细分析了系统有关的可靠性问题，不仅获得时刻ｔ系统失效的概率和（０，ｔ］中系统失效的平均次数的瞬态解，而且也获得其平稳结果。最后用数值计算比较了间歇开放系统和经典系统的差别。