中国广义回归抽样估计系统的构建及应用

在抽样理论和应用研究方面,中国一直比较重视抽样方案设计,而忽视抽样估计方法研究。本文在系统总结加拿大等西方国家成功经验的基础上,引入并改进了一套广义回归估计系统,应用在复杂的连续多阶抽样调查中。本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体模型进行扩展,建立各种类型的回归模型进行模型辅助的广义回归估计,最终形成一套广义回归估计系统,为中国抽样估计的应用研究奠定理论基础。最后,本文以中国农产量的连续多阶抽样调查为例,给出了具体的回归估计程序,从而验证这套系统的实践性和应用价值。     

LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed as an extension of NLMEs. These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard parametric NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. Previous estimation procedures are based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (SAEM) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We derive oracle inequalities for this nonparametric estimator. We combine the two approaches in a general estimation procedure that we illustrate with simulations and through the analysis of a real data set of price evolution in on-line auctions.     

系统性风险度量CoES的建模和检验

本文结合极值理论(Extreme Value Theory,EVT)和新的动态混合Copula(Dynamic Mixture Copula,DM-Copula)函数,提出了一种新的CoES估计方法DM-Copula-EVT。在EVT建模中,本文改进了阈值的选取方法以避免选择的主观性,并提出了一系列新的动态混合Copula以更好地刻画金融市场日益复杂的尾部关联性。此外,本文首次提出了检验CoES模型设定正确性的后验分析方法,包括无条件覆盖性检验和条件覆盖性检验。将本文建模和检验方法应用于我国金融市场,研究发现:相对于传统使用的t分布,EVT能更好地拟合指数的尾部分布;新的动态混合Copula函数能更好地刻画金融部门与系统之间的复杂关联性。     

An alternative derivation of the Kalman filter using the quasi-likelihood method

The Kalman filter gives a recursive procedure for estimating state vectors. The recursive procedure is determined by a matrix, so-called gain matrix, where the gain matrix is varied based on the system to which the Kalman filter is applied. Traditionally the gain matrix is derived through the maximum likelihood approach when the probability structure of underlying system is known. As an alternative approach, the quasi-likelihood method is considered in this paper. This method is used to derive the gain matrix without the full knowledge of the probability structure of the underlying system. Two models are considered in this paper, the simple state space model and the model with correlated between measurement and transition equation disturbances. The purposes of this paper are (i) to show a simple way to derive the gain matrix; (ii) to give an alternative approach for obtaining optimal estimation of state vector when underlying system is relatively complex.     

Prior Distributions for Item Parameters in IRT Models

The focus of this article is on the choice of suitable prior distributions for item parameters within item response theory (IRT) models. In particular, the use of empirical prior distributions for item parameters is proposed. Firstly, regression trees are implemented in order to build informative empirical prior distributions. Secondly, model estimation is conducted within a fully Bayesian approach through the Gibbs sampler, which makes estimation feasible also with increasingly complex models. The main results show that item parameter recovery is improved with the introduction of empirical prior information about item parameters, also when only a small sample is available.     

Complex Latent Variable Modeling in Educational Assessment

Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with powerful simulation-based estimation techniques are discussed. Furthermore, it is shown how the Bayes factor can be used to test relevant hypotheses in assessment using the College Basic Academic Subjects Examination (CBASE) data.     

Seemingly unrelated regression on the autoregressive (Ar(p)) singular equation system

This paper studies the estimation of seemingly unrelated regressions (SUR) of singular equation systems with an autoregressive error process (AR(p)) for each equation.Parameter estimates of the autoregressive singular equation system are not generally invariant to the equation deleted. Under the model specification restriction on the autoregressive parameters, the invariance property is preserved, and this paper shows that a single equation generalized least squares (GLS) estimation for a general autoregressive error process is equivalent to the SURGLS estimation of the AR(p) singular equation system.     

Poverty and inequality in European regions

The European Union Statistics on Income and Living Conditions (EU-SILC) is the main source of information about poverty and economic inequality in the member states of the European Union. The sample sizes of its annual national surveys are sufficient for reliable estimation at the national level but not for inferences at the sub-national level, failing to respond to a rising demand from policy-makers and local authorities. We provide a comprehensive map of median income, inequality (Gini coefficient and Lorenz curve) and poverty (poverty rates) based on the equivalised household income in the countries in which the EU-SILC is conducted. We study the distribution of income of households (pro-rated to its members), not merely its median (or mean), because we regard its dispersion and frequency of lower extremes (relative poverty) as important characteristics. The estimation for the regions with small sample sizes is improved by the small-area methods. The uncertainty of complex nonlinear statistics is assessed by bootstrap. Household-level sampling weights are taken into account in both the estimates and the associated bootstrap standard errors.     

Rapid detection of the switching point in a financial market structure using the particle filter

We apply the particle filter for the quick and accurate estimation of a switching point in a financial market based on a recently developed theoretical model, the potentials of unbalanced complex kinetics (PUCK) model, which fulfils all empirically stylized facts such as fat-tailed distribution of price changes and the anomalous diffusion in a short-time scale. We show the efficiency of an optimized driving force in particle filtering for the estimation of the parameters of the PUCK model, using a simulation study. As an example, we apply the method to the dollar–yen exchange market before and after the biggest earthquake in Japan in March 2011. With this fast and efficient estimation method, we can clearly confirm that the statistics of the time series of exchange rate changed drastically at the time of the arrival of the quake in Tokyo area, implying that the earthquake worked as a trigger for the market's switching point.     

高考填报志愿的综合决策模型

本文对高考填报志愿系统进行定量分析,采用模糊AHP方法设计了评价模型、灰色预测方法给出了预测模型,结合实例论述了模糊AHP以及灰色预测的基本过程,对填报高考志愿这个主客观信息综合集成的复杂过程具有一定的指导意义。     

Graphical technique for comparing designs for random models

Methods for comparing designs for a random (or mixed) linear model have focused primarily on criteria based on single-valued functions. In general, these functions are difficult to use, because of their complex forms, in addition to their dependence on the model's unknown variance components. In this paper, a graphical approach is presented for comparing designs for random models. The one-way model is used for illustration. The proposed approach is based on using quantiles of an estimator of a function of the variance components. The dependence of these quantiles on the true values of the variance components is depicted by plotting the so-called quantile dispersion graphs (QDGs), which provide a comprehensive picture of the quality of estimation obtained with a given design. The QDGs can therefore be used to compare several candidate designs. Two methods of estimation of variance components are considered, namely analysis of variance and maximum-likelihood estimation.     

Complex elliptical distributions with application to shape analysis

We introduce a general class of complex elliptical distributions on a complex sphere that includes many of the most commonly used distributions, like the complex Watson, Bingham, angular central Gaussian and several others. We study properties of this family of distributions and apply the distribution theory for modeling shapes in two dimensions. We develop maximum likelihood and Bayesian methods of estimation to describe shape and obtain confidence bounds and credible regions for shapes. The methodology is illustrated through an example where estimation of shape of mouse vertebrae is desired.     

Markov chain Monte Carlo estimation of a mixture item response theory model

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.     

Efficiencies in Variance Estimation for Complex Survey Data

Data from complex survey designs require special consideration, with regard to variance estimation and analysis, because of design components that include unequal selection probabilities, stratification, and clustering. Using data from the National Medical Care Expenditure Survey, which is characterized by a complex survey design, four variance estimation programs are compared: SESUDAAN/RATIOEST, SUPERCARP, PSALMS, and HESBRR. The comparisons concentrate on program capabilities, computational efficiency, and user facility.     

Self-weighted recursive estimation of GARCH models

The generalized autoregressive conditional heteroscedasticity (GARCH) processes are frequently used to investigate and model financial returns. They are routinely estimated by computationally complex off-line estimation methods, for example, by the conditional maximum likelihood procedure. However, in many empirical applications (especially in the context of high-frequency financial data), it seems necessary to apply numerically more effective techniques to calibrate and monitor such models. The aims of this contribution are: (i) to review the previously introduced recursive estimation algorithms and to derive self-weighted alternatives applying general recursive identification instruments, and (ii) to examine these methods by means of simulations and an empirical application.     

Assessing shape differences in populations of shapes using the complex watson shape distribution

This paper presents a novel Bayesian method based on the complex Watson shape distribution that is used in detecting shape differences between the second thoracic vertebrae for two groups of mice, small and large, categorized according to their body weight. Considering the data provided in Johnson et al. (1988), we provide Bayesian methods of estimation as well as highest posterior density (HPD) estimates for modal vertebrae shapes within each group. Finally, we present a classification procedure that can be used in any shape classification experiment, and apply it for categorizing new vertebrae shapes in small or large groups.     

On the estimation of homogeneous population size from a complex dual-record system

ABSTRACT

A dual-record system (DRS) (equivalently two sample capture–recapture experiments) model, with time and behavioural response variation, has attracted much attention specifically in the domain of official statistics and epidemiology, as the assumption of list independence often fails. The relevant model suffers from parameter identifiability problem, and suitable Bayesian methodologies could be helpful. In this article, we formulate population size estimation in DRS as a missing data problem and two empirical Bayes approaches are proposed along with the discussion of an existing Bayes treatment. Some features and associated posterior convergence for these methods are mentioned. Investigation through an extensive simulation study finds that our proposed approaches compare favourably with the existing Bayes approach for this complex model depending upon the availability of directional nature of underlying behavioural response effect. A real-data example is given to illustrate these methods.     

Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.     

ESTIMATING BAYESIAN NETWORKS FOR HIGH‐DIMENSIONAL DATA WITH COMPLEX MEAN STRUCTURE AND RANDOM EFFECTS

The estimation of Bayesian networks given high‐dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically assume that the data consist of independent and identically distributed samples. It is often the case, however, that the available data have a more complex mean structure, plus additional components of variance, which must then be accounted for in the estimation of a Bayesian network. In this paper, score metrics that take account of such complexities are proposed for use in conjunction with score‐based methods for the estimation of Bayesian networks. We propose first, a fully Bayesian score metric, and second, a metric inspired by the notion of restricted maximum likelihood. We demonstrate the performance of these new metrics for the estimation of Bayesian networks using simulated data with known complex mean structures. We then present the analysis of expression levels of grape‐berry genes adjusting for exogenous variables believed to affect the expression levels of the genes. Demonstrable biological effects can be inferred from the estimated conditional independence relationships and correlations amongst the grape‐berry genes.     

Investigate Data Dependency for Dynamic Gene Regulatory Network Identification through High-dimensional Differential Equation Approach

Gene regulation plays a fundamental role in biological activities. The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. We proposed a comprehensive statistical procedure for ODE model to identify the dynamic GRN. In this article, we applied this model to different segments of time course gene expression data from a simulation experiment and a yeast cell cycle study. We found that the two cell cycle and one cell cycle data provided consistent results, but half cell cycle data produced biased estimation. Therefore, we may conclude that the proposed model can quantify both two cell cycle and one cell cycle gene expression dynamics, but not for half cycle dynamics. The findings suggest that the model can identify the dynamic GRN correctly if the time course gene expression data are sufficient enough to capture the overall dynamics of underlying biological mechanism.