Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH

Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration-death, M/M/ 1 queue, linear birth-death and a branching diffusion process, among others, as special cases.     

Asymptotic properties of the maximum-likelihood estimator for a class of birth-and-death processes admitting a unique stationary distribution

The asymptotic properties of the maximum-likelihood estimator of the parameter vector for a class of birth-and-death processes admitting a unique stationary distribution are studied. Also, it is shown that identifiability of the parameter vector with respect to the likelihood implies that the Fisher information matrix is of full rank. Two special cases of biological interest are presented. One of these, the exponential birth-and-death process, is proposed as a more appropriate model of density dependence than the logistic process.     

层次分析法（AHP）在选择教材中的应用

选择教材是一个多目标决策问题．萨蒂的层次分析法提供了解决这类问题的一个方法．本文简要地介绍了层次分析法，并将其应用于数学教材的优选．     

Nonparametric estimation of the limiting availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.deceased after the paper was accepted     

Approximation spline de la prevision d'un processus fonctionnel autorégressif d'ordre 1

ABSTRACT We present a method to approximate and forecast, on an entire interval, a continuous-time process. For this purpose, we use the modelization of ARH(l) processes, defined by Bosq (1991). We deal with the practical problem of the discretization of the observed trajectories and approximate them by means of spline functions. We show by simulations that for well-chosen smoothing parameters, good prediction can be obtained in comparison with the “predictable” part of the process. Finally, we apply this model to forecast road traffic and compare it with a SARIMA model.     

Small-sample results for maximum-likelihood estimation in branching processes

In this article, small sample properties of the maximum-likelihood estimator (m.l.e.) for the offspring distribution (pk) and its mean m are considered in the context of the simple branching process. A representation theorem is given for the m.l.e. of (Pk) from which the m.l.e. of m is obtained. The case where p0 + p1 + p2 = 1 is studied in detail: numerical results are given for the exact bias of these estimators as a function of the age of the process; a curve fitting analysis expresses the bias of m? as a function of the mean and the variance of the offspring distribution and finally an “approximate m.l.e.” for (pk) is given.     

关于单叶函数的几点性质

设函数f(z)=z+a_2z~2+…在单位圆内解析单叶,记其族为S。对f(z)∈S,令φλ(z)=(f(z)/z)~λ=1+sum from 1 to ∞D_nZ~n。本文限制f(z)∈S(a)或Kc(a)(文中定义)条件下,获得β的上界,γ的下界,使t_n(λ)=||D_n(λ)|-|D_(n-1)(λ)||≤Aπ~(-β),sum fron 1 to ∞t(λ)<∞。     

Runaway Reactions, Their Courses, and the Methods to Establish Safe Process Conditions

The purpose of this paper is to describe the various process deviations which can cause a runaway reaction to occur, and to discuss the experimental information necessary for risk assessment, the choice of a safe process, and the mitigation of the consequences of the runaway reaction. Ten typical hazardous process situations have been identified, considering various modes of initiation, homogeneous and heterogeneous, Arrhenius, and autocatalytic reactions. Each possible hazardous process deviation is illustrated by examples from the process industry and/or relevant experimental information obtained from laboratory experiments.     

Judgment and Analysis in Oil Spill Risk Assessment

The risk of oil spills is a major environmental issue in the siting of proposed coastal refineries, oil terminals, deepwater ports, and in the leasing of offshore lands for oil exploration and development. As with any kind of risk, oil spill risk assessment is inherently judgmental and no analytic method can eliminate the need for judgment. This paper compares representative examples of oil spill risk assessments with regard to decisions about data, variables, functional relations, and uncertainty. The comparison emphasizes the judgmental basis of analytic methods.