洗衣机发展预测模型及应用

我国洗衣机的生产发展十分迅速,从1978年的年产400台到1985年的883万台,八年间增长二千多倍,今后的生产发展前景如何?运用本文介绍的一种预测模型,可以求得公元2000年以前每年洗衣机需求量的预测值,并求得1983年8月至1991年1月为洗衣机生产发展的成熟时期,该模型亦可用于其它耐用消费品的生产发展预测,所得结果可供有关部门决策时参考。     

收入分布函数在收入不平等研究领域的应用

收入分布函数的研究对于收入不平等的探讨意义重大,但是国内该领域的研究尚待进一步的拓展。笔者在文献回顾的基础上梳理了国外的相关研究,把常用的分布函数分成两参数分布和多参数分布函数两类,介绍了各类函数拟合居民实际收入分布的效果及其与基尼系数的关系;同时,本文剖析了各类函数之间的内在联系;进一步,基于分布函数的角度,笔者研究了收入流动性与收入不平等之间的联系,分析了平均数和中位数比值与基尼系数之间的数学关系以及如何利用该比值来估计分布函数的参数。利用这些研究结果,文章探讨了2010年我国城镇居民的收入结构和贫困问题并提出了一些前瞻性的研究建议。     

Asymptotic convergence of dimension reduction based boosting in classification

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method–dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.     

Estimation with right‐censored observations under a semi‐Markov model

The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada     

Generalized varying-coefficient single-index model

In this paper, the generalized varying-coefficient single-index model is discussed based on penalized likelihood. All the unknown functions are fitted by penalized spline. The estimates of the unknown parameters and the unknown coefficient functions are obtained and the estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. Two simulation studies are carried out to illustrate the performance of the estimates. An application of the model to the Hong Kong environmental data further demonstrates the potential of the proposed modelling procedures.     

Kernel Density-Based Linear Regression Estimate

For linear regression models with non normally distributed errors, the least squares estimate (LSE) will lose some efficiency compared to the maximum likelihood estimate (MLE). In this article, we propose a kernel density-based regression estimate (KDRE) that is adaptive to the unknown error distribution. The key idea is to approximate the likelihood function by using a nonparametric kernel density estimate of the error density based on some initial parameter estimate. The proposed estimate is shown to be asymptotically as efficient as the oracle MLE which assumes the error density were known. In addition, we propose an EM type algorithm to maximize the estimated likelihood function and show that the KDRE can be considered as an iterated weighted least squares estimate, which provides us some insights on the adaptiveness of KDRE to the unknown error distribution. Our Monte Carlo simulation studies show that, while comparable to the traditional LSE for normal errors, the proposed estimation procedure can have substantial efficiency gain for non normal errors. Moreover, the efficiency gain can be achieved even for a small sample size.     

The adaptive calibration of testing p-values

Abstract

In statistical hypothesis testing, a p-value is expected to be distributed as the uniform distribution on the interval (0, 1) under the null hypothesis. However, some p-values, such as the generalized p-value and the posterior predictive p-value, cannot be assured of this property. In this paper, we propose an adaptive p-value calibration approach, and show that the calibrated p-value is asymptotically distributed as the uniform distribution. For Behrens–Fisher problem and goodness-of-fit test under a normal model, the calibrated p-values are constructed and their behavior is evaluated numerically. Simulations show that the calibrated p-values are superior than original ones.     

Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.     

Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

This article discusses sampling plans, that is, the allocation of sampling units, for computing tolerance limits in a balanced one--way random-effects model. The expected width of the tolerance interval is derived and used as the basis for comparing different sampling plans. A well-known cost function and examples are used to facilitate the discussion.     

Likelihood Ratio Order of m-Spacings in Multiple-Outlier Models

This article deals with the multiple-outlier exponential model. The likelihood ratio order between m-spacings of the combined sample is developed, some results extend the conclusions on simple spacings in Wen et al. (2007 Wen , S. , Lu , Q. , Hu , T. ( 2007 ). Likelihood ratio order of spacings of heterogeneous exponential random variables . J. Multivariate Anal. 98 : 743 – 756 .[Crossref], [Web of Science ®] , [Google Scholar]).