A note on stable limit theory for the OLSE with non usual rates and the heteroskedasticity robust Wald test

We are occupied with an example concerning the limit theory of the ordinary least squares estimator (OLSE) when the innovation process of the regression has the form of a martingale transform the iid part of which lies in the domain of attraction of an α-stable distribution, the scaling sequence has a potentially diverging truncated α-moment, and the regressor process has a potentially divergent truncated second moment. We obtain matrix rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences, and stable limits. We also derive asymptotic exactness, consistency, and local asymptotic unbiasedness under appropriate local alternatives for a heteroskedasticity robust Wald test based on subsampling. The results could be useful for inference on the factor loadings in an instance of the APT model.     

The negative binomial–beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial–beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.     

Efficient regression modeling for correlated and overdispersed count data

Abstract

The objective of this paper is to propose an efficient estimation procedure in a marginal mean regression model for longitudinal count data and to develop a hypothesis test for detecting the presence of overdispersion. We extend the matrix expansion idea of quadratic inference functions to the negative binomial regression framework that entails accommodating both the within-subject correlation and overdispersion issue. Theoretical and numerical results show that the proposed procedure yields a more efficient estimator asymptotically than the one ignoring either the within-subject correlation or overdispersion. When the overdispersion is absent in data, the proposed method might hinder the estimation efficiency in practice, yet the Poisson regression based regression model is fitted to the data sufficiently well. Therefore, we construct the hypothesis test that recommends an appropriate model for the analysis of the correlated count data. Extensive simulation studies indicate that the proposed test can identify the effective model consistently. The proposed procedure is also applied to a transportation safety study and recommends the proposed negative binomial regression model.     

Zero-inflated Poisson and negative binomial integer-valued GARCH models

Zero inflation means that the proportion of 0's of a model is greater than the proportion of 0's of the corresponding Poisson model, which is a common phenomenon in count data. To model the zero-inflated characteristic of time series of counts, we propose zero-inflated Poisson and negative binomial INGARCH models, which are useful and flexible generalizations of the Poisson and negative binomial INGARCH models, respectively. The stationarity conditions and the autocorrelation function are given. Based on the EM algorithm, the estimating procedure is simple and easy to be implemented. A simulation study shows that the estimation method is accurate and reliable as long as the sample size is reasonably large. A real data example leads to superior performance of the proposed models compared with other competitive models in the literature.     

Management sampling for larvae of the colorado potato beetle

Summary Untreated plot of ‘Kennebec’ and ‘Superior’ potatoes were sampled for Colorado potato beetle (CPB) at L'Assomption, Quebec, in 1982, 1986 and 1987. Numbers of CPB larvae per stalk were counted on 74 occasions for sample sizes ranging from 50 to 200 stalks. Regression techniques were used to estimate the relationship between mean and cumulative proportion of stalks infected. These were used to set up binomial sequential probability ratio test (SPRT) sampling plans for pest management decision making with tally numbers (or tally thresholds, cutoff numbers) equal to 0,1,...10. A binomial scheme defined by tally number equal to 4 is proposed for general use, and corresponding plans are given, with estimated operating characteristic and average sample number curves.     

C2C 环境中顾客重复购买行为的实证与建模

通过分析C2C 商家的交易记录, 发现单个商家的顾客重复购买次数呈幂律分布, 这与重复购买理论以往得到的购买次数为负二项分布的结论不同. 基于C2C 交易的实际情况, 建立了具有购买强化效应的购买概率模型, 模型很好的解释了顾客重复购买率呈幂律分布的现象.实证和模型表明, C2C 环境中, 顾客购买次数的分布具有很长的尾部, 大量顾客有低的购买次数, 而少数顾客有很高的重复购买次数;模型还揭示了巨大的潜在顾客数量和顾客多次购买的强化效应是造成重复购买分布呈幂律形式的重要原因.     

风险投资灵活性价值探索

本文从西方经济学生产要素理论出发,深入挖掘了风险投资项目灵活性价值的源泉,并引入二叉树期权定价模型进一步给出了一种风险投资项目灵活性价值的定量评估方法,最后通过案例应用,有效解决了风险投资项目灵活性价值评估问题。     

CEV模型下有离散红利支付的几何平均亚式期权的定价

首先阐述了标准几何亚式期权的涵义及其定价模型,介绍了CEV的涵义,然后借助PhelimP.Boyle和Yisong Tian为CEV模型下回望期权和障碍期权的定价技巧,利用二叉树逼近方法得到服从CEV过程且有离散红利支付的几何平均亚式期权的定价。     

带有能力约束的多元马氏需求报童模型

在随机需求环境下考虑带有能力约束的多产品报童问题.为了对多产品的需求进行预测,并度量其需求间的关系,本文首先建立了多元马氏需求模型.其次,在该模型的理论基础上,提出了带有能力约束的多元马氏需求报童模型,进而给出多产品的最优订购策略解.最后,利用期望需求状态的概率值及其截尾概率分析了模型最优解的性质.模型的结论表明,在能力约束的条件下,最优订购量关于左截尾概率单调递减,关于右截尾概率单调递增,而期望需求状态的概率值对最优订购量具有双重的特殊影响.     

偏微分方程的非线性变换和精确解

利用截属的Painlev'e展开式、非线性变换和可积的微分方程，可以求出一类非线性偏微分方程的自Backlund变换和它的精确解，孤立波解。波动方程、Hirota-Satsuma方程组和非线性色散与耗散方程作为例子来说明这一方法。