A note on stable limit theory for the OLSE with non usual rates and the heteroskedasticity robust Wald test

We are occupied with an example concerning the limit theory of the ordinary least squares estimator (OLSE) when the innovation process of the regression has the form of a martingale transform the iid part of which lies in the domain of attraction of an α-stable distribution, the scaling sequence has a potentially diverging truncated α-moment, and the regressor process has a potentially divergent truncated second moment. We obtain matrix rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences, and stable limits. We also derive asymptotic exactness, consistency, and local asymptotic unbiasedness under appropriate local alternatives for a heteroskedasticity robust Wald test based on subsampling. The results could be useful for inference on the factor loadings in an instance of the APT model.     

The conditional maximum of Poisson random variables

The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied.     

Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter $\theta$ appearing in parabolic SPDEs of the form

$d{u}^{?}(t,x)=(A_0+\theta A_1)u^{?}(t,x)dt+?dW(t,x),$

where $A_0$ and$A_1$ are partial differential operators, $W$ is a cylindrical Brownian motion (CBM) and $?\downarrow 0$. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.     

Combining Multivariate Bioassays: Accurate Inference Using Small Sample Asymptotics

For several independent multivariate bioassays performed at different laboratories or locations, the problem of testing the homogeneity of the relative potencies is addressed, assuming the usual slope‐ratio or parallel line assay model. When the homogeneity hypothesis holds, interval estimation of the common relative potency is also addressed. These problems have been investigated in the literature using likelihood‐based methods, under the assumption of a common covariance matrix across the different studies. This assumption is relaxed in this investigation. Numerical results show that the usual likelihood‐based procedures are inaccurate for both of the above problems, in terms of providing inflated type I error probabilities for the homogeneity test, and providing coverage probabilities below the nominal level for the interval estimation of the common relative potency, unless the sample sizes are large, as expected. Correction based on small sample asymptotics is investigated in this article, and this provides significantly more accurate results in the small sample scenario. The results are also illustrated with examples.     

产权理论:马克思和科斯的比较(英文)

马克思用崭新的无产阶级世界观构建了产权理论大厦的主体工程。产权是所有制的法律形态。作为财产形式的法权关系,产权不但是反映经济关系的意志关系,而且是历史的产物和历史的范畴,具有历史的形式。马克思着重研究了资本主义的财产关系,即在揭示经济领域中资本和雇佣劳动之间对立关系的基础上,将价值增值过程表述为法学和产权理论中的所有权关系及其占有过程,涉及所有权、占有权、使用权、支配权、经营权、索取权、继承权等一系列权力的统一与分离,从而论证了资本主义财产关系和产权制度的阶级对抗性质。马克思揭示的从“消极扬弃”到“积极扬弃”的变革方向,把资本主义生产关系及其产权制度将被公有制的经济关系和法权关系所代替这一历史必然性和长期发展趋势清晰地呈现出来。     

Bayesian Treatment of Model Uncertainty for Partially Applicable Models

This article discusses how analyst's or expert's beliefs on the credibility and quality of models can be assessed and incorporated into the uncertainty assessment of an unknown of interest. The proposed methodology is a specialization of the Bayesian framework for the assessment of model uncertainty presented in an earlier paper. This formalism treats models as sources of information in assessing the uncertainty of an unknown, and it allows the use of predictions from multiple models as well as experimental validation data about the models’ performances. In this article, the methodology is extended to incorporate additional types of information about the model, namely, subjective information in terms of credibility of the model and its applicability when it is used outside its intended domain of application. An example in the context of fire risk modeling is also provided.     

均值——下偏距（M-LPM）组合优化下的两基金分离定理

通常的投资建议和两基金分离定理之间存在较大差异,这就是著名的Canner难题。厚尾分布以及投资者对风险的厌恶水平对真实的投资组合行为有显著的影响,在考虑下侧风险的情况下,本文关注投资者如何选择投资组合、两基金分离定理在什么情况下能够成立、以及对投资者的投资策略的选择的影响如何。当目标等于无风险利率时,有文献表明两基金分离定理可以在均值——下偏距（M-LPM）中得到证明。然而,除了以无风险利率为目标外,哪些其它的目标也可以使分离定理成立的问题已经出现。本文尝试回答这个问题,并对投资建议和两基金分离定理的差异给出了合理的解释。     

城市大气中污染物扩散的施密特数研究

借助反问题方法对风洞实验工况选取不同施密特数进行数值模拟试验,分析比较了不同施密特数时街道峡谷内各个观测点的数值模拟数据和风洞实验数据.研究结果表明,城市街道内大气污染物扩散的施密特数为0.7～0.8.