Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions

The aim of this paper is to find approximate log-transition density functions for multivariate time-inhomogeneous diffusions in closed form. There are many empirical evidences supporting that the data generating process governing dynamics of many economics variables might vary over time because of economic climate changes or time effects. One possible way to explain the time-dependent dynamics of state variables is to model the drift or volatility terms as functions of time t$t$ as well as state variables. A way to find closed-form likelihood expansion for a multivariate time-homogeneous diffusion has been developed by Aït-Sahalia (2008). This research is built on his work and extends his results to time-inhomogeneous cases. We conduct Monte Carlo simulation studies to examine performance of the approximate transition density function when it is used to obtain ML estimates. The results reveal that our method yields a very accurate approximate likelihood function, which can be a good candidate when the true likelihood function is unavailable as is often the case.     

Location decisions: The role of uncertainty about consumer tastes

This paper analyzes to what extent firms make decisions about location based on uncertainty about consumer tastes. The model used in this analysis incorporates a linear city and quadratic consumer-transportation costs. In this framework, when firms choose locations, or in other words, choose the kind of product they are going to manufacture, they ignore the location, or real tastes, of their consumers. The existence of uncertainty raises the degree of product differentiation, because the anti-competitive effect that arises as distance from rivals increases counteracts the reduction in the degree of differentiation provided by the demand effect.     

Likelihood Ratio Test for and Against Nonlinear Inequality Constraints

In applied statistics a finite dimensional parameter involved in the distribution function of the observed random variable is very often constrained by a number of nonlinear inequalities. This paper is devoted to studying the likelihood ratio test for and against the hypothesis that the parameter is restricted by some nonlinear inequalities. The asymptotic null distributions of the likelihood ratio statistics are derived by using the limits of the related optimization problems. The author also shows how to compute critical values for the tests.     

Tests of independence in a bivariate exponential distribution

The problem of testing independence in a two component series system is considered. The joint distribution of component lifetimes is modeled by the Pickands bivariate exponential distribution, which includes the widely used Marshall and Olkins distribution and the Gumbels type II distribution. The case of identical components is first addressed. Uniformly most powerful unbiased test (UMPU) and likelihood ratio test are obtained. It is shown that inspite of a nuisance parameter, the UMPU test is unconditional and this test turns out to be the same as the likelihood ratio test. The case of nonidentical components is also addressed and both UMPU and likelihood ratio tests are obtained. A UMPU test is obtained to test the identical nature of the components and extensions to the type II censoring scheme and multiple component systems are also discussed. Some modifications to account for the difference in parameters under test and use conditions are also discussed.     

Designs for Variance Components Estimation: Past and Present

This article provides (1) a comprehensive coverage of the literature on designs for estimating variance components, and (2) a review of recent applications of such designs in genetics, statistical process control, and quality improvement. In addition, recent methods of estimation of variance components and model forms, other than the linear, are discussed. The latter developments have a direct effect on the choice of design. Some suggested ideas for future research directions are also given.     

Using best–worst scaling to explore perceptions of relative responsibility for ensuring food safety

We examine stakeholders’ perceptions of the share of the overall responsibility of each stage in the food supply chain has in ensuring that the meat people cook and eat at home is safe to consume. We elicit these perceptions of relative responsibility via surveys using the best–worst scaling technique and analyse the data via Bayesian estimation of mixed logit models. Results are reported for two groups of stakeholders: consumers and farmers, and for two meat food chains: chicken and beef. The results reveal that consumers tend to think farmers are more responsible for ensuring meat safety than farmers do. Similarly, farmers tend to think consumers have a greater degree of responsibility than consumers believe they have themselves. Such beliefs might affect stakeholders’ willingness to take actions and reduce hazards in the supply chain. From a policy perspective, the research findings provide useful insights to support policymakers and other decision-makers in the industry in developing mitigation strategies. Communication with consumers and farmers about emerging food safety problems in a supply chain and their involvement in proactive practices would need to be attuned to their subjective perceptions of relative responsibilities in order for integrated risk management systems to be effective.     

基于PVECM的综列协整检验临界值的计算

Groen和Kleibergen(2003)基于综列数据的误差纠正模型(PVECM)和极大似然估计方法,提出了与时间序列中Johanson(1991)协整检验类似的综列协整检验。其似然比检验统计量的极限分布是维纳过程的泛函,所以其临界值需要通过仿真试验来计算,但Groen和Kleibergen(2003)既没有给出具体的临界值也没有给出具体的程序。本文通过对维纳过程的随机积分进行仿真,估计基于PVECM的综列协整检验的临界值。与现有的部分临界值的比较结果显示,我们的计算程序是正确的,计算结果是可靠的。     

On the simultaneous estimation of physical and monetary commodity flows

Large databases mapping commodity flows measured in various units such as currency, tons or caloric values are the backbone of many recent environmental-economic studies. Their construction typically requires combining large amounts of partial information in a series of successive steps. These include the estimation of unobserved flows, transformations between units, handling aggregation re-classification and, finally, reconciling estimates with mass, financial and/or energy balances. This paper proposes a maximum entropy model that allows for the simultaneous estimation of unobserved commodity flows as well as corresponding prices such that data constraints in various units of measurement, levels of aggregation and possibly mismatching classifications are simultaneously satisfied. Its capability is assessed through a Monte-Carlo analysis and its performance compared with a simple step-wise approach. Our results suggest that the simultaneous approach performs significantly better in a vast majority of cases.     

Properties of h-Likelihood Estimators in Clustered Data

We study properties of the maximum h-likelihood estimators for random effects in clustered data. To define optimality in random effects predictions, several foundational concepts of statistics such as likelihood, unbiasedness, consistency, confidence distribution and the Cramer–Rao lower bound are extended. Exact probability statements about interval estimators for random effects can be made asymptotically without a prior assumption. Using the binary-matched pair example, we illustrated that the use of random effects recover information, leading to the boon on estimating treatment effects.     

On the linear statistical relationship

The fitting of lines to data, when the relative precision of the measured data is a known constant, is a problem which is of some interest, for example in comparison of measurement procedures. We examine some ways of treating this problem with a view to clarifying the relationship of solutions with the Maximum Likelihood Estimate. Acknowledgement. I am grateful to Hans Schneeweiss for suggesting a strengthened form of the definition of f in Section 4.