On Existence of Maximum Likelihood Estimators in Exponential Families

We propose a simple necessary and sufficient condition for existence of maximum likelihood estimators in a large class of canonical exponential families. We give an application to log-spline families.     

A branching method for the fixed charge transportation problem

This paper presents a branching method for the solution of the fixed charge transportation problem. Starting with a linear formulation of the problem, we develop the method which converges to the optimal solution. The method is based on the computation of a lower bound and an upper bound embedded within a branching process. We present a detailed numerical example to illustrate the proposed method.     

Uncertainty about Uncertainty and Delay in Bargaining

We study a one‐sided offers bargaining game in which the buyer has private information about the value of the object and the seller has private information about his beliefs about the buyer's valuation. We show that this uncertainty about uncertainties dramatically changes the set of outcomes. In particular, second order beliefs can lead to a delay in reaching agreement even when the seller makes frequent offers. We show that not all types of second order beliefs lead to a delay. When the buyer assigns positive probability to the seller knowing the buyer's value, then delay not only can occur, but it must occur for a class of equilibria. However, in all other cases delay will never occur.     

友谊奖外国专家辽宁行——我的亲身感受

就在我刚结束在波兰的假期之时．我被告知国家外国专家局邀请我和夫人参加辽宁之行,这真是一个巨大的惊喜。我感到非常荣幸和高兴,因为在我5年的中国生活中,还从未到过辽宁。     

Does sequential augmenting of simple linear heteroscedastic regression reduce variances of ordinary least-squares estimators?

If uncorrelated random variables have a common expected value and decreasing variances, then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable variance reduction property (VRP) by augmenting data is not automatically inherited by ordinary least-squares (OLS) estimators of parameters. We derive a new decomposition for updating the covariance matrices of the OLS which implies conditions for the OLS to have the VRP. In particular, in the case of a straight-line regression, we show that the OLS estimators of intercept and slope have the VRP if the values of the explanatory variable are increasing. This also holds true for alternating two-point experimental designs.     

Comparison of Efficiency of Stratified and Unequal Probability Sampling

In this article, a choice of the optimum sampling design to study a finite population is studied. Three sampling schemes are compared, viz., Sunter's procedure of unequal probability sampling, stratified sampling under optimum stratification, and simple random sampling without replacement. The comparison is made against a background of various correlation between stratification and survey variables and various variability in the variables. Under weak correlation and large variability, stratification appeared to be more efficient than Sunter's procedure. Under strong correlation and/or low variability in the variables, the latter procedure was the most efficient. Simple random sampling was usually the least efficient.     

Ecological lands for conservation of vascular plant diversity in the urban environment

Conservation of biodiversity in urban areas has become crucial to urban green area management. There are several legislative solutions for preservation of species and habitats in cities. One of them is ‘ecological lands’ – a low-restrictive form of protected areas in Poland. We aimed to assess their efficiency in vascular flora biodiversity conservation in the urban environment in Poznań (W Poland; 550,000 inhabitants). We hypothesized that ecological lands which cover <2% of the city area comprise over 50% of taxonomic diversity and over 90% of functional trait-level range of the vascular flora. Analysis of five ecological lands, which covered 1.8% of the whole city area confirmed our hypothesis. In ecological lands studied, we found 564 species of vascular plants, which is 52.9% of the whole city flora. These species belonged to 23 of 29 phytosociological classes represented in the whole city (73.9%). Functional trait distributions in ecological lands studied comprised from 95.8 to 100% of trait distributions in the flora of the whole city. Ecological lands seem to be a good way for conservation of biodiversity in urban areas. The legislative simplicity and low restrictiveness for both land management and recreational utility make ecological lands a much easier form of nature conservation which may be adapted to other cities for more efficient biodiversity management.