Stabilization Coefficient of Random Variable

Coefficient of variation, standard deviation divided by mean, has some essential defects. Its density, expectation and variance are too complex to make the statistical inference for such a coefficient. The definition of stabilization coefficient is just the reciprocal of variation coefficient, mean divided by standard deviation. Such a coefficient has a simple expectation and a simple variance, and is an asymptotically unbiased estimator and a consistent estimator of its true value. Furthermore, coefficient of stabilization has an asymptotic normality. Due to its statistical advantages, coefficient of stabilization is easy to be tested statistically. In some applied fields, usually, there is an increasing standard deviation accompanying an increasing mean. Coefficient of stabilization can be practically used for some comparison studies in such fields. Illustrations about comparing microorganism strains are given in this paper. The robustness of stabilization coefficient is satisfactory.     

Effect of covariate omission in Weibull accelerated failure time model: A caution

The accelerated failure time model is presented as an alternative to the proportional hazard model in the analysis of survival data. We investigate the effect of covariates omission in the case of applying a Weibull accelerated failure time model. In an uncensored setting, the asymptotic bias of the treatment effect is theoretically zero when important covariates are omitted; however, the asymptotic variance estimator of the treatment effect could be biased and then the size of the Wald test for the treatment effect is likely to exceed the nominal level. In some cases, the test size could be more than twice the nominal level. In a simulation study, in both censored and uncensored settings, Type I error for the test of the treatment effect was likely inflated when the prognostic covariates are omitted. This work remarks the careless use of the accelerated failure time model. We recommend the use of the robust sandwich variance estimator in order to avoid the inflation of the Type I error in the accelerated failure time model, although the robust variance is not commonly used in the survival data analyses.     

-混合误差下非参数回归权函数估计的渐近正态性

本文在一定条件下讨论了－混合误差下非参数回归权函数估计的渐近正态性，并且减弱了文献［３］的条件，证明方法大大简化了。     

两个生物序列比对的个数的渐近值

利用发生函数给出了两个生物序列比对的个数的精确公式,并运用多元函数的渐近估计法计算它的渐近值.     

密度分布非均匀的害虫和天敌生态模型的平衡解的稳定性

讨论一类密度分布非均匀的害虫和天敌生态模型平衡解的稳定性，得到该问题非负平衡解的存在性、渐适性和相应吸引区域。     

The statistical dynamics of recurrent biological events

In this paper we develop a general modeling framework within which many models for systems which produce events at irregular times through a combination of probabilistic and deterministic dynamics can be comprehended. We state and prove new sufficient conditions for the global asymptotic behaviour of the density evolution in these systems, and apply our results to many previously published models for the cell division cycle. In addition, we develop a new interpretation for the statistics of action potential production in excitable cells.To whom correspondence should be sent     

A Stratified Product Limit Estimator for the Follow-up Study in Cardio-Thoracic Surgery

We propose a stratified product limit estimator and compare the asymptotic results with those of the unstratified version. When the censoring mechanisms are unequal for different strata, the unstratified version may overestimate the total survival rate of a heterogeneous population. A numerical example in cardiac surgery is examined to demonstrate that this situation does occur in real applications. This overestimation also can be elucidated heuristically by some redistribution schemes for the censored data.     

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

Semiparametric model-based inference in the presence of missing responses

We consider a semiparametric model that parameterizes the conditionaldensity of the response, given covariates, but allows the marginaldistribution of the covariates to be completely arbitrary. Responsesmay be missing. A likelihood-based imputation estimator anda semi-empirical-likelihood-based estimator for the parametervector describing the conditional density are defined and provedto be asymptotically normal. Semi-empirical loglikelihood functionsfor the parameter vector and the response mean are derived.It is shown that the two semi-empirical loglikelihood functionsare distributed asymptotically as weighted ² and scaled ², respectively.     

Solution of functional difference equations from behavioral theory

Behavioral models based on Markovian decision processes lead to functional difference equations for quantities such as the mean lifetime of the forager and the probability of reproductive success of the forager. In this paper, asymptotic and iterative methods are developed for the solution of such equations. The asymptotic methods are compared with numerical simulations. The iterative methods can be proved by a simple application of contraction mapping theorems.