Model selection: some generalized distributions

Many models have been used to represent the distributions of random variables in statistics, engineering, business, and the physical and social science. This paper considers two, four-parameter generalized bea distributions that include nearly all the models actually used as special or limiting cases. Properties and the interrelationships among these distributions are considered. Expressions are reported that facilitate parameter estimation and the analysis of associated means, variances, hazard functions and other distributional characteristics.

Estimation procedures corresponding to different data types are considered. Maximum likelihood estimation is used and the value of the likelihood function provides and important criterion for model selection. The relative performance of the various models is compared for several data sets.     

On selecting a subset containing the most probable multinomial event

Panchapakesan's procedure is considered for the problem of selectinga subset containing the most probable multinomial event. We use the type-2 Dirichlet integral to express the probability of a correct selection and propose a much simpler proof for the worst configuration. We also show that the supremum of the expected subset size occurs at the equal configuration.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Non-parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure

Abstract.  We consider the problem of estimating a collection of integrals with respect to an unknown finite measure μ from noisy observations of some of the integrals. A new method to carry out Bayesian inference for the integrals is proposed. We use a Dirichlet or Gamma process as a prior for μ , and construct an approximation to the posterior distribution of the integrals using the sampling importance resampling algorithm and samples from a new multidimensional version of a Markov chain by Feigin and Tweedie. We prove that the Markov chain is positive Harris recurrent, and that the approximating distribution converges weakly to the posterior as the sample size increases, under a mild integrability condition. Applications to polymer chemistry and mathematical finance are given.     

Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses

Abstract. A right‐censored version of a U ‐statistic with a kernel of degree m 1 is introduced by the principle of a mean preserving reweighting scheme which is also applicable when the dependence between failure times and the censoring variable is explainable through observable covariates. Its asymptotic normality and an expression of its standard error are obtained through a martingale argument. We study the performances of our U ‐statistic by simulation and compare them with theoretical results. A doubly robust version of this reweighted U ‐statistic is also introduced to gain efficiency under correct models while preserving consistency in the face of model mis‐specifications. Using a Kendall's kernel, we obtain a test statistic for testing homogeneity of failure times for multiple failure causes in a multiple decrement model. The performance of the proposed test is studied through simulations. Its usefulness is also illustrated by applying it to a real data set on graft‐versus‐host‐disease.     

Singular weighing designs and estimation of total weight

The problem of estimation of total weight of objects using a singular spring balance weighing design has been studied in this paper. A lower bound of the estimated total weight is obtained and some classes of designs attaining the lower bound are studied.     

On the numerical behaviour of ARMA(P,Q) covariance determinants for various sample sizes

An algorithm for the covariance determinant of a stationary autoregressive-moving average model is considered. Some asymptotic properties of this determinant in the stationarity and invertibil-ity region of the process are studied numerically in simple special cases.     

Confidence sets as programming problems

Optimizing criteria for choosing a confidence set for a parameter are formulated as mathematical programming problems. The two optimizing criteria, probability of coverage and size of set, give rise to a pair of inverse programming problems. Several examples are worked out. The programming problems are then formulated to allow the incorporation of partial information about the parameter. By varying the family of prior distributions, a continuum of problems from the frequency approach to a Bayesian approach is obtained. Some examples are considered in which the family of priors contains more than one but not all prior distributions.     

The inverse weighted Lindley distribution: Properties,estimation and an application on a failure time data

In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented. The maximum likelihood estimators for the parameters in the presence of complete and censored data are presented. Two corrective approaches are considered to derive modified estimators that are bias-free to second order. A numerical simulation is carried out to examine the efficiency of the bias correction. Finally, an application using a real data set is presented in order to illustrate our proposed distribution.     

论环境污染侵权因果关系的证明

环境污染问题是一个技术问题,同时也是一个法律问题。由于环境污染的特殊性和复杂性,在环境污染侵权纠纷中,按照传统的因果关系证明规则,受害者很难证明因果关系的存在,这使得环境法律制度的公平正义目标难以实现。因此,在环境污染侵权因果关系的证明中,采用盖然性证明标准、实行举证责任倒置及因果关系推定具有重要的意义。