Markov zero-inflated Poisson regression models for a time series of counts with excess zeros

This paper discusses a class of Markov zero-inflated Poisson regression models for a time series of counts with the presence of excess zero relative to a Poisson distribution, in which the frequency distribution changes according to an underlying two-state Markov chain. Features of the proposed model, estimation method based on the EM and quasi-Newton algorithms, and other implementation issues are discussed. A Monte Carlo study shows that the estimation method is accurate and reliable as long as the sample size is reasonably large, and the choice of starting probabilities for the Markov process has little impact on the parameter estimates. The methodology is illustrated using daily numbers of phone calls reporting faults for a mainframe computer system.     

基于小波多分辨分析的高阶矩CAPM

 为改进传统Beta系数测量系统风险的不足，反映系统风险的动态特征，讨论了四阶矩的资本资产定价模型(CAPM)并将小波分析引入到高阶矩CAPM研究中。利用小波多分辨分析的特点，给出了小波高阶中心矩和高阶混合中心矩的定义，基于此给出了多分辨系统风险测度Beta、Gamma、Theta的计算方法和多分辨CAPM，并从行为金融理论出发，给出多分辨高阶矩CAPM的金融背景解释。实证结果支持了多分辨系统风险假说和多分辨高阶矩CAPM的成立，为构建动态投资组合分散金融风险的动态影响提供了证据。     

下方资本资产定价模型及其实证分析

近30多年来,CAPM在广泛应用的同时也备受学者和实践者的争议,主要是方差作为计量风险的指标越来越受到质疑。文章以半方差作为计量风险的指标,得到建立在均值—半方差理论上的一个均衡定价模型———下方资本资产定价模型(D-CAPM),并以上海股票市场为例实证研究D-CAPM的优越性。     

非对称分布条件下的基金业绩测度

文章首先实证分析了以CAPM为理论基础的均方业绩测度方法的不足,提出收益分布非对称性条件下的基金业绩评价,并建议使用半方差调整期望收益来测度基金业绩,实证研究结果也支持了本观点。     

A two-phase approach to estimating time-varying parameters in the capital asset pricing model

Following the development of the economy and the diversification of investment, mutual funds are a popular investment tool nowadays. Choosing excellent targets from hundreds of mutual funds has become more and more crucial to investors. The capital asset pricing model (CAPM) has been widely used in the capital cost estimation and performance evaluation of mutual funds. In this study, we propose a new two-phase approach to estimating the time-varying parameters of CAPM. We implemented a simulation study to evaluate the efficiency of the proposed method and compared it with the commonly used state space and rolling regression methods. The results showed that the new method is more efficient in most scenarios. Meanwhile, the proposed approach is very practical and it is unnecessary to judge and adjust the estimating process for different situations. Finally, we applied the proposed method to equity mutual funds in the Taiwan stock market and reported the performances of two funds for demonstration.     

Bayesian analysis of single-molecule experimental data

Summary.  Recent advances in experimental technologies allow scientists to follow biochemical processes on a single-molecule basis, which provides much richer information about chemical dynamics than traditional ensemble-averaged experiments but also raises many new statistical challenges. The paper provides the first likelihood-based statistical analysis of the single-molecule fluorescence lifetime experiment designed to probe the conformational dynamics of a single deoxyribonucleic acid (DNA) hairpin molecule. The conformational change is initially treated as a continuous time two-state Markov chain, which is not observable and must be inferred from changes in photon emissions. This model is further complicated by unobserved molecular Brownian diffusions. Beyond the simple two-state model, a competing model that models the energy barrier between the two states of the DNA hairpin as an Ornstein–Uhlenbeck process has been suggested in the literature. We first derive the likelihood function of the simple two-state model and then generalize the method to handle complications such as unobserved molecular diffusions and the fluctuating energy barrier. The data augmentation technique and Markov chain Monte Carlo methods are developed to sample from the posterior distribution desired. The Bayes factor calculation and posterior estimates of relevant parameters indicate that the fluctuating barrier model fits the data better than the simple two-state model.     

动态资产定价理论中风险估计及其统计性质分析

一、引言古典资产定价理论,如Ｓｈａｒｐｅ的资产定价模型（ＣＡＰＭ）和Ｒｏｓ的套利定价理论（ＡＰＴ）,有助于大家对风险定价及其概念的理解。这些理论解释了资产回报的横截面行为,允许根据不同的风险水平对资产进行评价和计算。这些理论的经验证明必须对风险进行估...     

资本资产定价模型CAPM在中国资本市场中的实证检验

采用中国上海资本市场交易数据对资本资产定价模型（CAPM）的适用性进行了三个方面的检验：资产的风险和收益之间是否存在线性关系;系统风险是否是资产风险的唯一度量;资产的风险和收益是否正相关。结果发现：2003年8月1日至2006年7月31日期间,上海资本市场股票组合的平均超额收益率与其系统风险之间存在正相关关系,与非系统风险不存在显著的线性关系,基本符合标准形式的CAPM。这与国内许多学者对2001年以前中国资本市场CAPM的实证检验结果不太一致。     

Applying neural network Poisson regression to predict cognitive score changes

In this study, we combined a Poisson regression model with neural networks (neural network Poisson regression) to relax the traditional Poisson regression assumption of linearity of the Poisson mean as a function of covariates, while including it as a special case. In four simulated examples, we found that the neural network Poisson regression improved the performance of simple Poisson regression if the Poisson mean was nonlinearly related to covariates. We also illustrated the performance of the model in predicting five-year changes in cognitive scores, in association with age and education level; we found that the proposed approach had superior accuracy to conventional linear Poisson regression. As the interpretability of the neural networks is often difficult, its combination with conventional and more readily interpretable approaches under the generalized linear model can benefit applications in biomedicine.     

流动性信息与资产收益：基于非参数模型的分析

本文首先从全新的角度给出市场深度指标的求解方法,然后结合条件资产定价模型和自回归条件异方差模型的优势建立半变系数模型,并应用于我国股票市场每日收益率的研究,得出四点判断：1、通过非参数方法求解得到的指标值具有显著的平稳性。2、流动性信息的时变性对股票市场存在显著的非线性冲击,而且流动性信息的持续性变化与收益之间存在负向关系。3、得到和经典资产定价模型相同的结论,即市场综合指数对个股具有显著的影响。4、模型验证了流动性信息通过波动性将信息非线性传导给投资者的假设,伴随着流动性信息的时变性,投资者所得到的风险补偿也具备时变性。5、通过实际数据的验证,我们所建立的半变系数模型能够较好的解释流动性信息的传递,也为我们以后的实证研究提供了一个估计和检验流动性信息传导和时变型风险补偿的新方法。     

Poisson Regression and the Case-Crossover Design: Similarities and Differences

Poisson regression and case-crossover are frequently used methods to estimate transient risks of environmental exposures such as particulate air pollution on acute events such as mortality. Roughly speaking, a case-crossover design results from a Poisson regression by conditioning on the total number of failures. We show that the case-crossover design is somewhat more generally applicable than Poisson regression. Stratification in the case-crossover design is analogous to Poisson regression with dummy variables, or to a marked Poisson regression. Poisson regression makes it possible to express case-crossover likelihood functions as multinomial likelihoods without making reference to cases, controls, or matching. This derivation avoids the counterintuitive notion of basing inferences on exposures that occur post-failure.     

A class of correlated weighted Poisson processes

In this paper, we propose new classes of correlated Poisson processes and correlated weighted Poisson processes on the interval [0,1], which generalize the class of weighted Poisson processes defined by Balakrishnan and Kozubowski (2008), by incorporating a dependence structure between the standard uniform variables used in the construction. In this manner, we obtain another process that we refer to as correlated weighted Poisson process. Various properties of this process such as marginal and joint distributions, stationarity of the increments, moments, and the covariance function, are studied. The results are then illustrated through some examples, which include processes with length-biased Poisson, exponentially weighted Poisson, negative binomial, and COM-Poisson distributions.     

Use of an empirical probability generating function for testing a Poisson model

We present a test of the fit to a Poisson model based on the empirical probability generating function (epgf). We derive the limiting distribution of the test under the Poisson hypothesis and show that a rescaling of it is approximately independent of the mean parameter in the Poisson distribution. When inspected under a simulation study over a range of alternative distributions, we find that this test shows reasonable behaviour compared to other goodness-of-fit tests like the Poisson index of dispersion and smooth test applied to the Poisson model. These results illustrate that epgf-based methods for anlyzing count data are promising.     

Connections of the Poisson weight function to overdispersion and underdispersion

In this paper, we establish several connections of the Poisson weight function to overdispersion and underdispersion. Specifically, we establish that the logconvexity (logconcavity) of the mean weight function is a necessary and sufficient condition for overdispersion (underdispersion) when the Poisson weight function does not depend on the original Poisson parameter. We also discuss some properties of the weighted Poisson distributions (WPD). We then introduce a notion of pointwise duality between two WPDs and discuss some associated properties. Next, we present some illustrative examples and provide a discussion on various Poisson weight functions used in practice. Finally, some concluding remarks are made.     

Semiparametric estimation for count data through weighted distributions

This paper is concerned with semiparametric discrete kernel estimators when the unknown count distribution can be considered to have a general weighted Poisson form. The estimator is constructed by multiplying the Poisson estimate with a nonparametric discrete kernel-type estimate of the Poisson weight function. Comparisons are then carried out with the ordinary discrete kernel probability mass function estimators. The Poisson weight function is thus a local multiplicative correction factor, and is considered as the uniform measure to detect departures from the equidispersed Poisson distribution. In this way, the effects of dispersion and zero-proportion with respect to the standard Poisson distribution are also minimized. This method of estimation is also applied to the weighted binomial form for the count distribution having a finite support. The proposed estimators, in addition to being simple, easy-to-implement and effective, also outperform the competing nonparametric and parametric estimators in finite-sample situations. Two examples illustrate this new semiparametric estimation.     

非寿险费率厘定的索赔频率预测模型及其应用

在非寿险分类费率厘定中,泊松回归模型是最常使用的索赔频率预测模型,但实际的索赔频率数据往往存在过离散特征,使泊松回归模型的结果缺乏可靠性.因此,讨论处理过离散问题的各种回归模型,包括负二项回归模型、泊松-逆高斯回归模型、泊松-对数正态回归模型、广义泊松回归模型、双泊松回归模型、混合负二项回归模型、混合二项回归模型、Delaporte回归模型和Sichel回归模型,并对其进行系统比较研究认为:这些模型都可以看做是对泊松回归模型的推广,可以用于处理各种不同过离散程度的索赔频率数据,从而改善费率厘定的效果;同时应用一组实际的汽车保险数据,讨论这些模型的具体应用.     

Application of Multiple Imputation in Analysis of Data from Clinical Trials with Treatment Related Dropouts

This article develops a functional form of the generalized Poisson regression model that parametrically nests the Poisson and the two well known generalized Poisson regression models (GP-1 and GP-2). The proposed model is applied on the Malaysian motor insurance claim count data.     

A unified approach to estimating parameters in some generalized poission distributions

A family of distributions labelled as Poisson v Katz is formulated, which includes, as particular or limiting cases, the Negative Binomial, Neyman Type A, Poisson v Pascal, and Poisson v Binomial. Thus, while analyzing data, estimating the parameters in the Poisson v Katz family obviates the necessity of having to choose from among the particular or limiting cases. In this article minimum chi-square estimators are presented and their asymptotic relative efficiency obtained. An example is presented to illustrate the procedure     

零膨胀泊松模型的改进在零次索赔建模中的应用

零膨胀是非寿险精算中的一种常见现象,国内外许多学者对此进行了研究分析,而最具影响力的方法是零膨胀泊松模型与Hurdle模型,但这两个方法在区分零之间的差别时存在不足。实际中,产生零次索赔的保单持有人并非全部同质,如何提取零中所包含的信息对保险公司来说是重要的。鉴此,基于零膨胀泊松模型与Hurdle模型的思想,提出修正的零膨胀泊松模型,并利用非寿险精算中的实际数据,对新模型进行了拟合分析。与零膨胀泊松模型拟合结果的比较说明,修正的零膨胀模型在零的处理上更符合实际情况,更能体现零中所包含的信息。