中国股票市场的非线性分析

大多数时间序列往往具有变方差的非线性特性,即某些时期的波动特别剧烈,而另一时期的波动又相对平 稳。对中国股票市场的非线性现象进行分析,发现上证综合指数和深证成分指数分布显示中国股票市场非线性现 象十分明显。在分析数据的基础上,建立了上证综合指数和深证成分指数的广义自回归条件异方差(GARCH)和 自回归移动平均(ARMA)预测模型,并分析了中国股票市场的几个非线性特征。     

基于递归效用函数的两个代理人间的最优财富分配

在递归效用函数的基础上,讨论了两个代理人间的最优财富分配问题,将最优问题转化为动态方程.通过动态方程的求解过程,得到一个可加效用中得不到的性质,即代理人的期望剩余效用越高,其选择当期消费就会越高.     

Risk of Extreme Events in Multiobjective Decision Trees Part 2. Rare Events

Earlier work with decision trees identified nonseparability as an obstacle to minimizing the conditional expected value, a measure of the risk of extreme events, by the well-known method of averaging out and folding back. This second of two companion papers addresses the conditional expected value that is defined as the expected outcome assuming that a random variable is observed only in the upper 100 (1 −α) percent of potential outcomes, where α is a cumulative probability preselected by the decision maker. An approach is proposed to overcome the need to evaluate all policies in order to identify the optimal policy. The approach is based in part on approximating the conditional expected value by using statistics of extremes. An existing convenient approximation of the conditional expected value is shown to be separable into two constituent elements of risk and can thus be optimized, along with other objectives including the unconditional expected value of the outcome, in a multiobjective decision tree. An example of sequential decision making for remediation or environmental contamination is provided. The importance of the results for risk analyis beyond the minimization of conditional expected values is pointed out.     

Distribution Analyzer and Risk Evaluator (DARE) Using Fault Trees

Risk and uncertainty are integral parts of modern technology, and they must be managed effectively to allow the development of reliable, high-quality products. Because so many facets of technology and society involve risk and uncertainty, it is essential that risk management be handled in a systematic manner. Fault-tree analysis is one of the principal methods used in the analysis of systems'safety. Its detailed and systematic deductive structure makes it a valuable tool for design and diagnostic purposes. Point probability and the minimization of the expected failure probability have, until recently, dominated fault-tree analysis. A methodology that incorporates uncertainty analysis, conditional expected risk, and multiple objectives with fault-tree analysis is presented. A computer software package termed the "Distribution Analyzer and Risk Evaluator (DARE) Using Fault Trees," which translates the new methodology into a working decision-support system, is developed. DARE Using Fault Trees is a flexible computer code that is capable of analyzing the risk of the overall system in terms of the probability density function of failure probability. Emphasis is placed on the uncertainty and risk of extreme events. A comparative study between existing codes for fault-tree analysis and DARE demonstrates the strengths of the methodology. A case study for NASA's solid rocket booster is used to perform the comparative analysis.     

A measure of aliasing and applications to two-level fractional factorials

This paper examines some properties of a measure of aliasing proposed by Hedayat, Raktoe, and Federer (1974). It is shown that in the case of balanced orthogonal designs with no repeated treatments, minimizing the alias measure is equivalent to minimizing tr Yar(ψ). Lower bounds are found for fixed eigenvalues of the design matrix. These results are applied to two-level fractional factorials to show that in certain cases classical fractional-factorial designs yield minimal solutions for the alias measure.     

Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two-Dimensional Marginals

This paper considers a connected Markov chain for sampling 3 × 3 ×K contingency tables having fixed two‐dimensional marginal totals. Such sampling arises in performing various tests of the hypothesis of no three‐factor interactions. A Markov chain algorithm is a valuable tool for evaluating P‐values, especially for sparse datasets where large‐sample theory does not work well. To construct a connected Markov chain over high‐dimensional contingency tables with fixed marginals, algebraic algorithms have been proposed. These algorithms involve computations in polynomial rings using Gröbner bases. However, algorithms based on Gröbner bases do not incorporate symmetry among variables and are very time‐consuming when the contingency tables are large. We construct a minimal basis for a connected Markov chain over 3 × 3 ×K contingency tables. The minimal basis is unique. Some numerical examples illustrate the practicality of our algorithms.     

On the stability of maximum-likelihood estimators of orthogonal parameters

If two parameters ψ and λ, are orthogonal, λψ, the maximum-likelihood estimate of λ for given ψ, varies only slowly with ψ in the neighbourhood of the overall maximum-likelihood point. The same is true if ψλ is replaced by a nonlinear function h(ψλ). The detailed form of the variation of ψλ with ψ is studied, and a basis suggested for choosing a particular function h(ψλ) that shows the dependence in the least informative fashion.     

Conditional mean residual life functions

In this paper a conditional mean residual life in the context of reliability theory is introduced. The properties of the conditional mean residual life are studied. Various characterizations by the conditional mean residual life are proposed.     

Empirical bayes estimation of a distribution function with a gamma process prior

A sequence of empirical Bayes estimators is given for estimating a distribution function. It is shown that ‘i’ this sequence is asymptotically optimum relative to a Gamma process prior, ‘ii’ the overall expected loss approaches the minimum Bayes risk at a rate of n , and ‘iii’ the estimators form a sequence of proper distribution functions. Finally, the numerical example presented by Susarla and Van Ryzin ‘Ann. Statist., 6, 1978’ reworked by Phadia ‘Ann. Statist., 1, 1980, to appear’ has been analyzed and the results are compared to the numerical results by Phadia     

Alternative definitions of bivariate equilibrium distributions

The concept of equilibrium distribution plays an important role in survival analysis, reliability and insurance studies. If we consider the problem of extending this concept to higher dimensions, we do not have a unique solution. In this paper, alternative definitions of bivariate equilibrium distributions are studied and proposed. The Navarro et al. (2006) proposal is considered and some new results are given. We continue with the Gupta and Sankaran's (1998) definition. Necessary and sufficient conditions for its existence are stated and a characterization theorem is given. As a third alternative, a new definition based on conditional specification is introduced and several results are obtained. Reliability properties of the different versions are studied.