A Bayes Theorem Urn Model Optimization Problem

An urn model is a finite collection of indistinguishable urns together with an arbitrary distribution of a finite number of balls (bills) of k colors (denominations) into the urns. A Bayes theorem expectation optimization problem associated with certain urn models is discussed.     

Recursive Estimation of GARCH Models

This article develops three recursive on-line algorithms, based on a two-stage least squares scheme for estimating generalized autoregressive conditionally heteroskedastic (GARCH) models. The first one, denoted by 2S-RLS, is an adaptation of the recursive least squares method for estimating autoregressive conditionally heteroskedastic (ARCH) models. The second and the third ones (denoted, respectively, by 2S-PLR and 2S-RML) are adapted versions of the pseudolinear regression (PLR) and the recursive maximum likelihood (RML) methods to the GARCH case. We show that the proposed algorithms give consistent estimators and that the 2S-RLS and the 2S-RML estimators are asymptotically Gaussian. These methods seem very adequate for modeling the sequential feature of financial time series, which are observed on a high-frequency basis. The performance of these algorithms is shown via a simulation study.     

Empirical Study of Six Tests for Equality of Populations with Zero-Inflated Continuous Distributions

We evaluated the properties of six statistical methods for testing equality among populations with zero-inflated continuous distributions. These tests are based on likelihood ratio (LR), Wald, central limit theorem (CLT), modified CLT (MCLT), parametric jackknife (PJ), and nonparametric jackknife (NPJ) statistics. We investigated their statistical properties using simulated data from mixed distributions with an unknown portion of non zero observations that have an underlying gamma, exponential, or log-normal density function and the remaining portion that are excessive zeros. The 6 statistical tests are compared in terms of their empirical Type I errors and powers estimated through 10,000 repeated simulated samples for carefully selected configurations of parameters. The LR, Wald, and PJ tests are preferred tests since their empirical Type I errors were close to the preset nominal 0.05 level and each demonstrated good power for rejecting null hypotheses when the sample sizes are at least 125 in each group. The NPJ test had unacceptable empirical Type I errors because it rejected far too often while the CLT and MCLT tests had low testing powers in some cases. Therefore, these three tests are not recommended for general use but the LR, Wald, and PJ tests all performed well in large sample applications.     

委托代理关系中的激励和监督

在道德风险问题的委托代理关系中,委托人对代理人行动的监督与对自然状态的观测所起的效果是等价的。本文考虑到委托人对自然状态的观测成本,提出了“状态观测模型”,并对信息不对称问题作了贝叶斯分析,讨论了不同观测力度对代理人努力水平、风险成本和代理成本等的作用。本文还给出了委托人愿意对自然状态进行观测的条件 -“愿意观测集。”     

Efficiency with Endogenous Population Growth

In this paper, we generalize the notion of Pareto efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed: ℘‐efficiency and 𝒜‐efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto efficiency when fertility is exogenous. We prove a version of the first welfare theorem for Barro–Becker type fertility choice models and discuss how this result can be generalized. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and we classify them into settings where inefficiencies arise inside the family and settings where they arise across families.     

Quantitative comparisons between finitary posterior distributions and Bayesian posterior distributions

The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable a posteriori quantities, which is very attractive in applications. Hence, with a view to a reconciliation between these two aspects of the Bayesian way of reasoning, in this paper we provide quantitative comparisons between posterior distributions of finitary parameters and posterior distributions of allied parameters appearing in usual statistical models.     

二阶常微分方程组边值问题正解的存在性

利用锥上不动点定理,研究了一类二阶非线性常微分方程组四点边值问题正解的存在性.在非线性项满足一定增长的条件下,得到了至少一个和两个正解存在的几个充分条件.     

Repeated Games with Differential Time Preferences

When players have identical time preferences, the set of feasible repeated game payoffs coincides with the convex hull of the underlying stage- game payoffs. Moreover, all feasible and individually rational payoffs can be sustained by equilibria if the players are sufficiently patient. Neither of these facts generalizes to the case of different time preferences. First, players can mutually benefit from trading payoffs across time. Hence, the set of feasible repeated game payoffs is typically larger than the convex hull of the underlying stage-game payoffs. Second, it is not usually the case that every trade plan that guarantees individually rational payoffs can be sustained by an equilibrium, no matter how patient the players are. This paper provides a simple characterization of the sets of Nash and of subgame perfect equilibrium payoffs in two-player repeated games.     

交错级数敛散性的一个判别定理

提出了交错级数敛散性的一个新的判别定理.该定理的判别式为极限形式,运用其判别交错级数的敛散性非常简便.