Estimating the Basic Reproductive Number in the General Epidemic Model with an Unknown Initial Number of Susceptible Individuals

Abstract. In any epidemic, there may exist an unidentified subpopulation which might be naturally immune or isolated and who will not be involved in the transmission of the disease. Estimation of key parameters, for example, the basic reproductive number, without accounting for this possibility would underestimate the severity of the epidemics. Here, we propose a procedure to estimate the basic reproductive number ( R ₀ ) in an epidemic model with an unknown initial number of susceptibles. The infection process is usually not completely observed, but is reconstructed by a kernel‐smoothing method under a counting process framework. Simulation is used to evaluate the performance of the estimators for major epidemics. We illustrate the procedure using the Abakaliki smallpox data.     

A Class of Non-parametric Tests in the Competing Risks Model for Comparing Two Samples

We consider a model when a process involving the production of elements is under inspection. The elements have possible failures due to competing risks. We assume the availability of a data set of failure times, D₁, obtained when the process is under control. Our main goal is to test if the failure rates in D₁ are equal to or less than the failure rates in another data set D₂, against "undesirable" neighbouring alternatives. A class of tests based on a two-dimensional vector statistic is obtained. Linear test statistics with weight functions giving optimal local asymptotic power are derived. Martingale techniques are used. An example illustrates the derivation of reasonable tests     

Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ-optimality

Ergodic diffusions in several dimensions, depending on an unknown multivariate parameter are considered. For estimation, when the diffusion is observed only at finitely many equidistant time points, unbiased estimating functions leading to consistent and asymptotically Gaussian estimators are used. Different types of estimating functions are discussed and the concept of small Δ-optimality is introduced to help select good estimating functions. Explicit criteria for small Δ-optimality are given. Also some exact optimality conditions are presented as well as, for one-dimensional diffusions, methods for improving estimators using time reversibility.     

GOODNESS OF FIT TESTS FOR HETEROGENEITY IN A CAPTURE-RECAPTURE EXPERIMENT

A class of goodness of fit tests is proposed to test for heterogeneity in a population in a capture-recapture experiment when individuals' capture intensities may depend on time in an unspecified manner.     

On almost sure convergence for sums of stochastic sequence

In this work we discuss almost sure convergence for sums of arbitrarily dependent stochastic sequence under different conditions of Chung’s type. Our approach is based on the stopping time technique and the theorem of convergence for martingale difference sequence. Meanwhile, the results here include some relevant classical conclusions.     

Space-time estimation of a particle system model

Let X be a discrete time contact process (CP) on ?², as defined by Durrett and Levin (1994, Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London Series B, 343, 329–350). We study the estimation of the model based on space-time evolution of X, that is, T + 1 successive observations of X on a finite subset S of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when T→∞, this estimator is consistent and asymptotically normal for a non-vanishing supercritical CP. Numerical studies confirm these theoretical ones.     

利率期限结构模型估计结果影响因素经验研究

本文首先将利率期限结构模型分成了四类,并总结了国内外利率期限结构模型的估计方法。作者利用中美利率数据证明了利率市场的有效性,估计方法和数值优化算法都会对模型估计结果产生影响。实证结果表明,利用所有市场利率数据的新估计方法得到的参数会更加准确,可以消除利率市场的套利机会;遗传算法的估计结果不太稳定,单纯形法估计结果对初始值比较敏感,而矩形分割法的估计结果最为稳健。     

An extension of a change-point problem

We consider a specific classification problem in the context of change-point detection. We present generalized classical maximum likelihood tests for homogeneity of the observed sample in a simple form which avoids the complex direct estimation of unknown parameters. This paper proposes a martingale approach to transformation of test statistics. For sequential and retrospective testing problems, we propose the adapted Shiryayev–Roberts statistics in order to obtain simple tests with asymptotic power one. An important application of the developed methods is in the analysis of exposure's measurements subject to limits of detection in occupational medicine.     

On bates of convergence in the central limit theorem for parameter estimation in general autoregressive model

This paper explores the rate at which the estimates of the unknown parameters in an autoregressive process converge in distribution to the normal variate.