A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time

American options in discrete time can be priced by solving optimal stopping problems. This can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data, and then we apply smoothing spline regression estimates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. We present results concerning consistency and the estimates’ rate of convergence.     

Improved model selection criteria for SETAR time series models

The purpose of this paper is threefold. First, we obtain the asymptotic properties of the modified model selection criteria proposed by Hurvich et al. (1990. Improved estimators of Kullback-Leibler information for autoregressive model selection in small samples. Biometrika 77, 709–719) for autoregressive models. Second, we provide some highlights on the better performance of this modified criteria. Third, we extend the modification introduced by these authors to model selection criteria commonly used in the class of self-exciting threshold autoregressive (SETAR) time series models. We show the improvements of the modified criteria in their finite sample performance. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error (RMSE) of prediction improves for the efficient criteria. These results are illustrated via simulation with SETAR models in which we assume that the threshold and the parameters are unknown.     

Empirical Bayes estimation in finite population sampling under functional measurement error models

The paper considers simultaneous estimation of finite population means for several strata. A model-based approach is taken, where the covariates in the super-population model are subject to measurement errors. Empirical Bayes (EB) estimators of the strata means are developed and an asymptotic expression for the MSE of the EB estimators is provided. It is shown that the proposed EB estimators are “first order optimal” in the sense of Robbins [1956. An empirical Bayes approach to statistics. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, pp. 157–164], while the regular EB estimators which ignore the measurement error are not.     

Affiliation networks with an increasing degree sequence

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this article, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We establish the uniform consistency and asymptotic normality of the maximum likelihood estimator when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results.     

论“三个代表”重要思想与马克思主义的一脉相承性

"三个代表"重要思想与马克思主义、毛泽东思想、邓小平理论是一脉相承的科学理论 体系,它以马克思主义的科学性为理论前提,以社会主义的改革实践为依据,以中国共产党人的 创新精神为内在动力,集中体现了马克思主义的立场、观点和方法,是对马克思主义、毛泽东思 想、邓小平理论的继承和发展。     

Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

EGARCH Model with Weighted Liquidity

We analyze a variant of the EGARCH model which captures the variation of the intra-day price. We study the asymptotic behavior of the estimators for the parameters of the model. We also illustrate our theoretical results by empirical studies.     

Data-driven tests of uniformity on product manifolds

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are reviewed and their large-sample asymptotic properties are given. A variant which is suitable for product manifolds is introduced. Data-driven goodness-of-fit tests of multivariate distributions are derived from data-driven tests of uniformity on tori.     

An exact test for nbue class of survival functions

Let F(x) be a life distribution. An exact test is given for testing H₀ F is exponential, versusH₁Fε NBUE (NWUE); along with a table of critical values for n=5(l)80, and n=80(5)65. An asymptotic test is made available for large values of n, where the standardized normal table can be used for testing.     

朱熹关于世界的统一性与多样性——“理一分殊说”

"理一"不是实体,是极好致善的"表德",即人类共同的价值标准。"分殊"是万物的个体性、多样性和差异性。理一与分殊的关系不是概念论的一般与个别的关系,是生命论的整体与分体的关系。理一在万物中,在人的心灵中。"理一分殊"说不只是从概念"推下来",而且是从经验"推上去",是经验与观念的统一,分析与综合的统一。人人有真、善、美的价值诉求,但最重要的是理会多样性,立足于分殊而理会理一。理一作为生命的根本法则就是仁,其实现的方法是"忠恕",只有尊重事物的差异性,从中理会一贯的道理,才能实现共同价值。朱子从生命哲学的立场,试图为人类生活建立统一的价值法则,直接讨论人类生存方式这一重大课题,并深入到心灵世界的深处,挖掘共同的生命诉求,坚持多样性是人类存在的基本形态,通过多样性的实践而实现共同价值,有其重要意义。