自回归模型选择的多准则方法

模型选择是建立时间序列模型的基础.文章将AR模型选择转化为多目标决策问题,并采用熵值法定权进行求解,在此基础上建立了模型选择的多准则方法,从而有效的解决了模型选择问题.该方法还可推广到滑动平均自回归(ARMA)的选择,由此提供了一条普遍适用的建模思路.     

非正态分布下具有自回归误差项的空间自回归模型变量选择研究

将变量选择引入空间计量模型,讨论具有自回归误差项的空间自回归模型的变量选择问题。在残差非正态独立同分布的条件下,通过最大化信息熵,提出空间信息准则,并证明其在该模型变量选择中具有一致性。模拟研究结果表明:无论对单个系数还是对全部系数,空间信息准则都能很好识别,且与经典的赤池准则相比具有较大的优势。因此,空间信息准则是一种更为有效的变量选择方法。     

基于极差的条件自回归极差模型

本文介绍了一种在固定时间区间上资产价格极差的动态模型:条件自回归极差(CARR)模型。CARR模型的条件极差十分类似GARCH模型中的条件方差,而且CARR模型也相似于ACD(Autoregressive Conditional Duration)模型。极端值理论(Extreme value theory)暗示极差是波动的一种有效估计,因此CARR模型可以看作是波动模型,并通过实证分析发现CARR模型的样本期外波动的预测效果比标准的GARCH波动模型要好。     

样本选择模型的一个简单半参数估计量

本文发展了一个针对样本选择模型的两阶段半参数估计量,其首先在第一阶段基于对数欧几里得分布差异测度估计离散选择概率,进而在第二阶段利用非参数sieve方法估计一个包含参数和非参数部分的部分线性模型以得到模型参数的估计。相对于文献中已有的半参数估计量,该估计量的计算更加简便,且计算负担相对较小。我们说明了该半参数估计量的一致性和渐近正态性,同时给出了其渐近方差的计算公式。蒙特卡洛模拟结果符合我们的理论结论。     

平滑转换自回归模型的单位根检验问题研究

 内容提要：针对非线性模型的单位根检验中存在的问题,本文认为非线性模型的单位根检验不应该在AR模型中进行,而应该在非线性模型中进行。以LSTAR(1)模型为例,本文给出了在其中进行单位根检验的统计量及其临界值。用蒙特卡洛试验证实,本文提出的单位根检验统计量的功效明显高于DF单位根检验,只有当非平稳特征十分明显时,DF检验才能检测出其中的单位根,因此,在非线性模型中进行单位根检验是必要的。     

基于风险价值约束的投资组合选择模型

把VaR风险度量和最优投资组合选择问题相结合,建立并求解了最优均值-VaR投资组合选择模型,实证检验所得到的结果中可以看出,以均值-VaR的模式来对资产进行优化配置具有较高效率,其效率超过以Markowitz均值进行的配置,通过-VaR的模式进行的配置,如果是在确定置信度的前提下,可以使个别偏好、共同偏好合为一体.在VaR的约束下M-V模型的特征,对于Markowitz均值方差的投资组合模型来说,是一种理论上得到的发展.     

样本选择参数分位回归模型及其在工资分布分解中的应用

在工资差距分解问题中,研究者经常会遇到样本选择偏差问题,直接忽略会导致最终估计结果产生严重偏差,同时在众多工资差距分解方法中,相比于均值分解,分布分解方法更受研究者青睐。针对参数分位回归,本文首次提出可加形式与非可加形式的样本选择参数分位回归（SSPQR）模型,并基于这两类样本选择参数分位回归模型给出修正样本选择偏差后的参数分位回归工资差距分布分解方法。运用上述方法及已有的工资分布分解方法,借助CHNS2015年度城镇数据,本文研究了我国城镇男女工资差距及差距分解问题,得出以下结论：①男女工资差距主要来源是性别歧视问题;②经过样本选择偏差修正后,实际的工资差距更大,歧视问题更严重;③男女工资差距程度在不同分位点上结果不同,换句话说,我们不能简单地仅从平均水平来判断工资差距程度;④与其他已有方法计算结果比较发现,SSPQR计算的工资差距程度更大。     

第三产业增加值的闭环门限自回归预测模型

文章利用非线性模型的逐段线性化方法研究了1978～2006年国内生产第三产业交通运输、仓储和邮政业与批发和零售业增加值的团环门限自回归(TAKSC)模型,并用所建模型对未来2007～2008年增加值进行外延预测.     

基于MCMC模拟的贝叶斯分层信用风险评估模型

缺少违约数据与债务人异质性是度量信用风险时面临的重要问题。贝叶斯模型中分层先验信息和马尔可夫链蒙特卡罗（MCMC）模拟方法的应用可以有效缓解数据缺失和测量误差问题,并能对债务人异质性进行评价和比较,从而避免低估风险。针对银行数据的模型拟合与模型诊断均展现了分层估计的适应性和灵活性,相关方法简洁清晰,利于国内风险分析人员采用。同时,涵盖宏观经济协变量的贝叶斯分层模型可以用于更加复杂的风险分析。     

基于平衡样本的最优模型辅助抽样策略

模型辅助方法的思想是基于抽样设计借助于超总体模型获得对总体参数的有效推断.满足辅助变量的HT估计等于总体总量真值的样本被称为平衡样本.对于平衡样本,如果超总体模型的异方差性可以通过辅助变量解释,由此得出最优抽样策略:平衡抽样设计与HT估计结合是最优策略,包含概率正比于模型残差的标准差.     

Uniform Ergodicity of the Particle Gibbs Sampler

The particle Gibbs sampler is a systematic way of using a particle filter within Markov chain Monte Carlo. This results in an off‐the‐shelf Markov kernel on the space of state trajectories, which can be used to simulate from the full joint smoothing distribution for a state space model in a Markov chain Monte Carlo scheme. We show that the particle Gibbs Markov kernel is uniformly ergodic under rather general assumptions, which we will carefully review and discuss. In particular, we provide an explicit rate of convergence, which reveals that (i) for fixed number of data points, the convergence rate can be made arbitrarily good by increasing the number of particles and (ii) under general mixing assumptions, the convergence rate can be kept constant by increasing the number of particles superlinearly with the number of observations. We illustrate the applicability of our result by studying in detail a common stochastic volatility model with a non‐compact state space.     

Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers

In Markov chain Monte Carlo analysis, rapid convergence of the chain to its target distribution is crucial. A chain that converges geometrically quickly is geometrically ergodic. We explore geometric ergodicity for two-component Gibbs samplers (GS) that, under a chosen scanning strategy, evolve through one-at-a-time component-wise updates. We consider three such strategies: composition, random sequence, and random scans. We show that if any one of these scans produces a geometrically ergodic GS, so too do the others. Further, we provide a simple set of sufficient conditions for the geometric ergodicity of the GS. We illustrate our results using two examples.     

Analysis of the Gibbs sampler for a model related to James-Stein estimators

We analyse a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these results to baseball data from Efron and Morris (1975). For a different range of prior distributions, we prove that the Gibbs sampler will fail to converge, and use this information to prove that in this case the associated posterior distribution is non-normalizable.     

Steady-state Gibbs sampler estimation for lung cancer data

This paper is based on the application of a Bayesian model to a clinical trial study to determine a more effective treatment to lower mortality rates and consequently to increase survival times among patients with lung cancer. In this study, Qian et al. [13 J. Qian, D.K. Stangl, and S. George, A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, in Bayesian Biostatistics, D. Berry and D. Stangl, eds., Marcel Dekker, New York, 1996, pp. 187–205. [Google Scholar]] strived to determine if a Weibull survival model can be used to decide whether to stop a clinical trial. The traditional Gibbs sampler was used to estimate the model parameters. This paper proposes to use the independent steady-state Gibbs sampling (ISSGS) approach, introduced by Dunbar et al. [3 M. Dunbar, H.M. Samawi, R. Vogel, and L. Yu, A more efficient Gibbs sampler estimation using steady state simulation: Application to public health studies, J. Stat. Simul. Comput. 10.1080/00949655.2013.770857.[Taylor &; Francis Online] , [Google Scholar]], to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in this application.     

Subsampling the Gibbs Sampler

This article provides a justification of the ban against sub-sampling the output of a stationary Markov chain that is suitable for presentation in undergraduate and beginning graduate-level courses. The justification does not rely on reversibility of the chain as does Geyer's (1992) argument and so applies to the usual implementation of the Gibbs sampler.     

Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the regression coefficients and Cholesky decompositions of the covariance matrix of the errors. Numerical simulations with artificially generated data show that the proposed method is effective in selecting the data-generating model restrictions and improving the forecasting performance of the model. Applying the method to daily foreign exchange rate data, we conduct stochastic search on a VAR model with stochastic conditional volatilities.     

Slow convergence of the Gibbs sampler

We consider the Gibbs sampler as a tool for generating an absolutely continuous probability measure ≥ on R^d. When an appropriate irreducibility condition is satisfied, the Gibbs Markov chain (X_n;n ≥ 0) converges in total variation to its target distribution ≥. Sufficient conditions for geometric convergence have been given by various authors. Here we illustrate, by means of simple examples, how slow the convergence can be. In particular, we show that given a sequence of positive numbers decreasing to zero, say (b_n;n ≥ 1), one can construct an absolutely continuous probability measure ≥ on R^d which is such that the total variation distance between ≥ and the distribution of X_n, converges to 0 at a rate slower than that of the sequence (b_n;n ≥ 1). This can even be done in such a way that ≥ is the uniform distribution over a bounded connected open subset of R^d. Our results extend to hit-and-run samplers with direction distributions having supports with symmetric gaps.     

A more efficient Gibbs sampler estimation using steady-state simulation: applications to public health studies

Markov chain Monte Carlo methods, in particular, the Gibbs sampler, are widely used algorithms both in application and theoretical works in the classical and Bayesian paradigms. However, these algorithms are often computer intensive. Samawi et al. [Steady-state ranked Gibbs sampler. J. Stat. Comput. Simul. 2012;82(8), 1223–1238. doi:10.1080/00949655.2011.575378] demonstrate through theory and simulation that the dependent steady-state Gibbs sampler is more efficient and accurate in model parameter estimation than the original Gibbs sampler. This paper proposes the independent steady-state Gibbs sampler (ISSGS) approach to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in multidimensional problems.     

Convergence of Slice Sampler Markov Chains

We analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we demonstrate that the algorithm is stochastically monotone, and we deduce analytic bounds on the total variation distance from stationarity of the method by using Foster–Lyapunov drift condition methodology.     

Markov-chain monte carlo: Some practical implications of theoretical results

We review and discuss some recent progress in the theory of Markov-chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.