The concept of risk unbiasedness in statistical prediction

This paper extends the concept of risk unbiasedness for applying to statistical prediction and nonstandard inference problems, by formalizing the idea that a risk unbiased predictor should be at least as close to the “true” predictant as to any “wrong” predictant, on the average. A novel aspect of our approach is measuring closeness between a predicted value and the predictant by a regret function, derived suitably from the given loss function. The general concept is more relevant than mean unbiasedness, especially for asymmetric loss functions. For squared error loss, we present a method for deriving best (minimum risk) risk unbiased predictors when the regression function is linear in a function of the parameters. We derive a Rao–Blackwell type result for a class of loss functions that includes squared error and LINEX losses as special cases. For location-scale families, we prove that if a unique best risk unbiased predictor exists, then it is equivariant. The concepts and results are illustrated with several examples. One interesting finding is that in some problems a best unbiased predictor does not exist, but a best risk unbiased predictor can be obtained. Thus, risk unbiasedness can be a useful tool for selecting a predictor.     

具p-Laplace算子型边值问题解的存在性

将具p-Laplace算子的边值问题转化成算子方程,对于p的不同取值给出适当的条件.利用Mawhin连续引理的推广形式,证明了一类具p-Laplace算子的微分方程边值问题解的存在性,得到了一系列解存在的充分条件.     

Shareholder Value and the Transformation of the U.S. Economy, 1984–20001

Using data from 62 U.S. industries for 1984–2000, this article explores the connections between shareholder value strategies, such as mergers and layoffs, and related industry‐level changes, such as de‐unionization, computer technology, and profitability. In line with shareholder value arguments, mergers occurred in industries with low profits, and industries where mergers were active subsequently saw an increase in layoffs. Industries with a high level of mergers increased investment in computer technology. This technology displaced workers through layoffs and was focused on reducing unionized workforces. Contrary to shareholder value arguments, there is no evidence that mergers or layoffs returned industries to profitability.     

公共行政当局以合同方式雇用人员时各类合同的适用范围

现时澳门公共行政当局以合同方式雇用人员的情况普遍,但是使用的合同类型多样,各类合同应有的不同适用范围卻鲜见有本地法律学术论文对此进行研究。本文尝试根据澳门现行法律和法学理论分析不同的合同各自应有的适用范围,并探讨该等合同在现行澳门法律下可能存在著的潜在问题。     

Central limit theorems of range-based estimators for diffusion models

Abstract

In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator.     

Optimum Experimental Designs for Choosing Between Competitive and Non Competitive Models of Enzyme Inhibition

In the study of the inhibition of enzyme reactions the Michaelis–Menten model is extended to include two experimental variables and three or more parameters. We combine the three-parameter models for competitive and non competitive inhibition in a four-parameter model and use optimum design theory to find D- and Ds-optimum designs for discriminating between the models. These designs are compared with compound T-optimum designs which provide the most powerful tests for discrimination between models. A single design is found with high discrimination efficiency whichever model is true.     

Semiparametric test for multiple change-points based on empirical likelihood

In the dynamic financial market, the change of financial asset prices is always described as a certain random events which result in abrupt changes. The random time when the event occurs is called a change point. As the event happens, in order to mitigate property damage the government should increase the macro-control ability. As a result, we need to find a valid statistical model for change point problem to solve it effectively. This paper proposes a semiparametric model for detecting the change points. According to the research of empirical studies and hypothesis testing we acquire the maximum likelihood estimators of change points. We use the loglikelihood ratio to test the multiple change points. We obtain some asymptotic results. The estimated change point is more efficient than the non parametric one through simulation experiments. Real data application illustrates the usage of the model.     

对偶基矢量组在张量分析中的作用与意义

在数学上将客观定律用量的分量形式表达为对坐标系具有不变性的方程，是张量分析所要解决的核心问题，为此，需从单一一的基矢量组发展为对偶的两个基矢量组，文中给地偶基几何意义解释的新证明，进一步阐明了“同变”与“逆变”的含义，说明“同变”较为现在广泛使用的     

Some Estimates for the Rate of Convergence in the Multidimensional Central Limit Theorem for Homogeneous Markov Chains

This paper obtains some estimates for the rate of convergence in the multi-dimensional central limit theorem for vector-valued functions of a homogeneous Markov chain without assuming the finiteness of their absolute third moment. These estimates have a universal character and generalize the results that hold when the third moments are finite.