Isotonic L2-projection test for local monotonicity of a hazard

We introduce a test statistic for testing the null hypothesis that the sampling distribution has a strictly increasing hazard rate on a specified interval [a,b]$[a,b]$. It is based on a comparison of the empirical distribution function with a shape-constrained estimate, using the restriction that the hazard is increasing. Its asymptotic (normal) distribution was recently derived in Groeneboom and Jongbloed (submitted for publication). We discuss a bootstrap method for computing the critical values and compare the test, thus obtained, with other recently proposed methods in a simulation study. Moreover, we prove that the bootstrap method works asymptotically. In proving that the (smooth and isotonic) bootstrap method works, we derive some results that seem to be of independent interest.     

Approximating Symmetric Distributions via Sampling and Coefficient of Variation

Abstract

The Coefficient of Variation is one of the most commonly used statistical tool across various scientific fields. This paper proposes a use of the Coefficient of Variation, obtained by Sampling, to define the polynomial probability density function (pdf) of a continuous and symmetric random variable on the interval [a, b]. The basic idea behind the first proposed algorithm is the transformation of the interval from [a, b] to [0, b-a]. The chi-square goodness-of-fit test is used to compare the proposed (observed) sample distribution with the expected probability distribution. The experimental results show that the collected data are approximated by the proposed pdf. The second algorithm proposes a new method to get a fast estimate for the degree of the polynomial pdf when the random variable is normally distributed. Using the known percentages of values that lie within one, two and three standard deviations of the mean, respectively, the so-called three-sigma rule of thumb, we conclude that the degree of the polynomial pdf takes values between 1.8127 and 1.8642. In the case of a Laplace (μ, b) distribution, we conclude that the degree of the polynomial pdf takes values greater than 1. All calculations and graphs needed are done using statistical software R.     

A new absolute continuous bivariate generalized exponential distribution

The generalized exponential is the most commonly used distribution for analyzing lifetime data. This distribution has several desirable properties and it can be used quite effectively to analyse several skewed life time data. The main aim of this paper is to introduce absolutely continuous bivariate generalized exponential distribution using the method of Block and Basu (1974). In fact, the Block and Basu exponential distribution will be extended to the generalized exponential distribution. We call the new proposed model as the Block and Basu bivariate generalized exponential distribution, then, discuss its different properties. In this case the joint probability distribution function and the joint cumulative distribution function can be expressed in compact forms. The model has four unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. To compute the maximum likelihood estimators directly, one needs to solve a four dimensional optimization problem. The EM algorithm has been proposed to compute the maximum likelihood estimations of the unknown parameters. One data analysis is provided for illustrative purposes. Finally, we propose some generalizations of the proposed model and compare their models with each other.     

A note about calibrated prediction regions and distributions

In this work we address the problem of the construction of prediction regions and distribution functions, with particular regard to the multidimensional setting. Firstly, we define a simple procedure for calculating the predictive distribution function which gives improved prediction limits. Secondly, with a multivariate generalization of a result presented in Ueki and Fueda (2007), we propose a method for correcting estimative prediction regions, to reduce their coverage error to the third-order accuracy. The improved prediction regions and the associated distribution functions are easy to calculate using a suitable bootstrap procedure. Examples of application are included, showing the good performance of the proposed method, even if we consider an approximated model for prediction purposes.     

Is There a “Pessimistic” Bias in Individual Beliefs? Evidence from a Simple Survey

It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win $10\texttt{C}\!\!\!\rule[2.3pt]{.4em}{.3pt}\!\!\rule[3.3pt]{.4em}{.3pt}It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win . How many times do you think that you will win?” The average answer is surprisingly about 3.9 which is below the average 5, and we interpret this as a pessimistic bias. We find that women are more “pessimistic” than men, as are old people relative to young. We also analyze how our notion of pessimism is related to more general notions of pessimism previously introduced in psychology.     

公司债务期限结构与违约风险

在资产风险水平、负债比率等因素一定的情况下,短期债务比例与违约概率呈类U形关系,基于风险规避角度的最优债务期限结构是存在的,并且这一最优短期债务比例与资产风险水平正相关,与负债比率负相关.我国上市公司短期债务比例普遍较高,根据理论预测和实证检验得出,进一步提高短期债务比例将会使公司违约风险继续扩大,进而危及我国的信用体系和金融秩序.     

开放式创新下的知识治理——基于认知视角的跨案例研究

开放式创新作为21世纪的创新趋势,所带来的挑战已经不是知识管理层面的问题,而是组织知识治理层面的问题,即迫切需要有效的治理机制来应对由知识差异性、知识复杂性以及创新者利益冲突所产生的知识基础性风险,从而为这种分布式、大规模的创新活动提供制度性保障.本文基于内涵更加丰富的认知视角,将知识治理的两种主要思路--情景组合观与流程设计观有机融合,以开放式创新中的知识流转作为分析单元,以创新过程各个环节中的知识基础性风险为分析的微观基础与治理对象,运用跨案例研究,旨在超越交易成本理论的传统思路建立一个开放式创新下知识治理的理论框架,从而为更加深入的实证研究奠定基础,也为企业的开放式创新实践提供有益的借鉴与参考.     

范·弗拉森后现代语言概率真理论的建构逻辑与反思

在当代西方科学哲学对真理问题的探索中,传统的基础主义的线式决定符合真理论受到质疑与颠覆,后现代的非线性建构主义真理观走向前台。美国当代科学哲学家范.弗拉森作为后现代建构主义真理观的翘楚从后现代建构主义立场出发,吸收20世纪以来统计物理学、相对论、概率论、语义学和语用学研究的最新成果,批判了基础主义实在论的线性符合真理观,提出了非线性的语义和语用概率真理论以及语境具体真理观。为了更好地坚持和发展马克思主义的真理观,使马克思主义真理观建立在当代自然科学最新成果诸如相对论、统计物理学、概率论、信息论的成果之上,我们要批判借鉴后现代主义概率真理论和语用、语境真理论,反对真理观上的线性决定论,正确处理反映与建构、确定与不确定、线性与非线性的辩证关系,丰富马克思主义真理观。     

A finite population quantile estimation by unequal probability sampling

Abstract

Using a model-assisted approach, this paper studies asymptotically design-unbiased (ADU) estimation of a population “distribution function” and extends to deriving an asymptotic and approximate unbiased estimator for a population quantile from a sample chosen with varying probabilities. The respective asymptotic standard errors and confidence intervals are then worked out. Numerical findings based on an actual data support the theory with efficient results.     

The large sample coverage probability of confidence intervals in general regression models after a preliminary hypothesis test

We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given value in a general regression model. Previously, this large sample coverage probability could only be estimated by simulation. Our formula only requires the evaluation, by numerical integration, of either a double or a triple integral, irrespective of the dimension of this specified vector parameter. We illustrate the application of this formula to a confidence interval for the odds ratio of myocardial infarction when the exposure is recent oral contraceptive use, following a preliminary test where two specified interactions in a logistic regression model are zero. For this real‐life data, we compare this large sample coverage probability with the actual coverage probability of this confidence interval, obtained by simulation.