An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.     

Empirical Likelihood Inference for the Rao‐Hartley‐Cochran Sampling Design

The Hartley‐Rao‐Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley‐Rao‐Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re‐sampling, linearization, variance estimation, design‐effects or joint inclusion probabilities.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

Latent transition models with latent class predictors: attention deficit hyperactivity disorder subtypes and high school marijuana use

Summary.  Attention deficit hyperactivity disorder (ADHD) is a neurodevelopmental disorder which is most often diagnosed in childhood with symptoms often persisting into adulthood. Elevated rates of substance use disorders have been evidenced among those with ADHD, but recent research focusing on the relationship between subtypes of ADHD and specific drugs is inconsistent. We propose a latent transition model (LTM) to guide our understanding of how drug use progresses, in particular marijuana use, while accounting for the measurement error that is often found in self-reported substance use data. We extend the LTM to include a latent class predictor to represent empirically derived ADHD subtypes that do not rely on meeting specific diagnostic criteria. We begin by fitting two separate latent class analysis (LCA) models by using second-order estimating equations: a longitudinal LCA model to define stages of marijuana use, and a cross-sectional LCA model to define ADHD subtypes. The LTM model parameters describing the probability of transitioning between the LCA-defined stages of marijuana use and the influence of the LCA-defined ADHD subtypes on these transition rates are then estimated by using a set of first-order estimating equations given the LCA parameter estimates. A robust estimate of the LTM parameter variance that accounts for the variation due to the estimation of the two sets of LCA parameters is proposed. Solving three sets of estimating equations enables us to determine the underlying latent class structures independently of the model for the transition rates and simplifying assumptions about the correlation structure at each stage reduces the computational complexity.     

关于我国股指期货设计方案的几点建议

本文主要阐述了作者对我国股指期货设计方案的一些看法。关于指数选择问题,本文认为不宜将现有的股价指数直接作为期货合约的交易基础,而应在对沪深两地现有成分股指数进行调整的基础上合成一个新指数;关于期货合约的设计,本文认为在确定乘数,最小波动点,合约交割月份,保证全水平及每日涨跌幅限制时,既要参考发达国家的经验,又要结合我国的国情;关于交易场所的选择,本文认为上海期货交易所应是首选。     

The Beta Product Distribution with Complex Parameters

The family consisting of the distributions of products of two independent beta variables is extended to include cases where some of the parameters are not positive but negative or complex. This “beta product” distribution is expressible as a Meijer G function. An example (from risk theory) where such a distribution arises is given: an infinite sum of products of independent random variables is shown to have a distribution that is the product convolution of a complex-parameter beta product and an independent exponential. The distribution of the infinite sum is a new explicit solution of the stochastic equation X = (in law) B(X + C). Characterizations of some G distributions are also proved.     

中国功能性分配格局的国际比较研究

 在当前的研究文献中,我国学者在对中国劳动收入份额进行国际比较时,通常在两个方面产生混乱：一是我国收入法GDP中的劳动者报酬指标包含了非公司业主的混合收入,采用的是宽口径的概念,而SNA1993中的雇员报酬概念却并不包括混合收入,是窄口径的概念。因此,根据我国收入法GDP数据直接计算出的劳动收入份额并不具有国际可比性;二是2004年我国收入法GDP的统计口径本身发生了变动,使得我国2004年前后的劳动收入份额也不具有可比性。本文首先以2004年的经济普查数据为基础,对自我雇佣者的混合收入按照宽、中、窄三种口径进行调整,基本消除了上述的两个不可比因素;其次,以调整后的可比数据为基础,本文对我国宽、中、窄口径的劳动收入份额进行了全面的国际比较,得到的结论更为稳健可靠。结果发现：如果采用窄口径的劳动报酬概念,我国的劳动收入份额不仅低于发达国家的平均水平15～20个百分点,也低于发展中国家的平均水平超过4个百分点。     

多项式、线性方程组及范德蒙行列式的相互应用

本文试图探讨多项式、线性方程组、范德蒙行列式的相互应用,从而揭示了它们的相互关系.     

一类二阶拟线性微分方程的非振动定理

考虑二阶拟线性微分方程 :( |y′|α -1y′)′+q(t) |y|α -1y=0 ,获得了在 q(t)振动的条件下该方程非振动的一些充分 (必要 )条件 ,改进和推广了已有文献的结果     

一类地下水水质污染问题广义解的唯一性及对初值和自由项的连续依赖性

本文讨论了一类地下水水质污染问题，其数学模型为一组非线性双曲—抛物耦合方程组，并证明了在相应初边值条件下广义解的唯一性及对初值和自由项的连续依赖性．