Model-cum-design-based estimation of the prevalence rate of a disease in a locality using spatial smoothing

In this article, we study the problem of estimating the prevalence rate of a disease in a geographical area, based on data collected from a sample of locations within this area. If there are several locations with zero incidence of the disease, the usual estimators are not suitable and so we develop a new estimator, together with an unbiased estimator of its variance, which may be appropriately used in such situations. An application of this estimator is illustrated with data from a large-scale survey, which was carried out in the city of Kolkata, India, to estimate the prevalence rate of stroke. We show that spatial modelling may be used to smooth the observed data before applying our proposed estimator. Our computations show that this smoothing helps to reduce the coefficient of variation and such a model-cum-design-based procedure is useful for estimating the prevalence rate. This method may of course be used in other similar situations.     

Estimating a uniform distribution when data are measured with a normal additive error with unknown variance

The problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered. The main purpose is to analyse the maximum-likelihood (ML) estimator and to compare it with the moment-method estimator. It is shown that this two-parameter model is regular so that the ML estimator is asymptotically efficient. Necessary and sufficient conditions are given for the existence of the ML estimator. As numerical problems are known to frequently occur while computing the ML estimator in this model, useful suggestions for computing the ML estimator are also given.     

Fitting DNA sequences through log-linear modelling with linear constraints

For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using φ-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.     

Efficiency of an almost unbiased two-parameter estimator in linear regression model

This paper deals with parameter estimation in the linear regression model and an almost unbiased two-parameter estimator is introduced. The performance of this new estimator over the ordinary least-squares estimator and the two-parameter estimator [M.R. Özkale and S. Kaçiranlar, The restricted and unrestricted two-parameter estimator, Comm. Statist. Theory Methods 36 (2007), pp. 2707–2725] in terms of scalar mean-squared error criterion is investigated and a simulation study is done.     

A dual problem of calibration of design weights

In this note, a dual problem to the calibration of design weights of the Deville and Särndal [Calibration estimators in survey sampling, J. Amer. Statist. Assoc. 87 (1992), pp. 376–382] method has been considered. We conclude that the chi-squared distance between the design weights and the calibrated weights equals the square of the standardized Z-score obtained by the difference between the known population total of the auxiliary variable and its corresponding Horvitz and Thompson [A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc. 47 (1952), pp. 663–685] estimator divided by the sample standard deviation of the auxiliary variable to obtain the linear regression estimator in survey sampling.     

Marcinkiewicz–Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators

Both Marcinkiewicz–Zygmund strong laws of large numbers (MZ-SLLNs) and ordinary strong laws of large numbers (SLLNs) for plug-in estimators of general statistical functionals are derived. It is used that if a statistical functional is ‘sufficiently regular’, then an (MZ-)SLLN for the estimator of the unknown distribution function yields an (MZ-)SLLN for the corresponding plug-in estimator. It is in particular shown that many L-, V- and risk functionals are ‘sufficiently regular’ and that known results on the strong convergence of the empirical process of α-mixing random variables can be improved. The presented approach does not only cover some known results but also provides some new strong laws for plug-in estimators of particular statistical functionals.     

抽样调查中的校准估计法

本文梳理总结了校准估计法自首次提出以来的研究成果。理论方法的发展集中在最短距离法、工具向量法和模型校准法三种校准方法的研究上;方法应用的发展体现在对简单参数和复杂参数的校准估计上。对小域估计、无回答、二重抽样等特定抽样问题和总体分位数、总体方差估计中校准估计法的具体应用作了重点梳理介绍。对校准估计法的理论和应用研究前景作了展望。     

无偏灰色Verhulst直接建模模型及其优化

针对本身已经具有饱和状态过程且近似满足Logistic函数形式的原始序列,提出通过对其进行倒数生成,建立无偏灰色Verhulst直接建模模型,并在此基础上将同时优化背景值和灰导数与利用"最小一乘法"确定响应系数的方法相结合,从而建立了优化的无偏灰色Verhulst直接建模模型。结果表明,该模型对满足Logistic函数形式的曲线进行模拟和预测具有完全重合性。通过实例分析说明了优化的新模型的可行性和有效性。     

关于多维指标抽样调查中删除指标的均值估计

针对多维度指标抽样调查情况,运用多变量幂函数逼近理论,对多指标中删除的指标构造出一类依赖于保留指标的估计量,通过对其性质的讨论,得出了该估计量的抽样误差与样本量的倒数同阶的结论。在抽样调查的实际应用中,可以根据给定的抽样误差,对部分指标进行调查,未被调查指标的均值通过调查指标值的估计去实现,从而达到了解全部指标信息的目的。