Towards a Routine External Evaluation Protocol for Small Area Estimation

Statistical criteria are needed by which to evaluate the potential success or failure of applications of small area estimation. A necessary step to achieve this is a protocol—a series of steps—by which to assess whether an instance of small area estimation has given satisfactory results or not. Most customary attempts at evaluation of small area techniques have deficiencies. Often, evaluation is not attempted. Every small area study requires an external evaluation. With proper planning, this can be routinely achieved, although at some cost, amounting to some sacrifice of efficiency of global estimates. We propose a Routine External Evaluation Protocol to allow us to judge whether, in a given survey, small area estimation has led to accurate results and sound inference.     

Predicting the sample mean by extreme order statistics

Summary This paper considers the prediction of the sample mean by extreme order statistics when the population distribution is known. The predictor and its mean square error are found. The problem is studied in details for the normal model.     

Estimation after sequential selection and ranking

Problems of estimating parameters from normal populations after the completion of the purely sequential selection and ranking methodology are addressed. Various second-order asymptotic characteristics associated with natural estimators are presented.     

On estimating the reliability after sequentially estimating the mean: The exponential case

Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.     

基于DMC-Ⅱ数码航空摄影测量区域网布设研究

从航空摄影到基础地理信息数据产品的获取包括航空摄影、地面控制、空三加密、内业测图等几个阶段。相片控制测量是航空摄影测量的基础工作,通过空三加密获得内业测图所需的外方位元素数据。随着DMC等数字航摄仪应用到航测生产领域当中,DMC影像数据在全数字摄影测量中发挥了越来越重要的作用。本文利用DMC-II数码航空影像,通过实验对DMC-II数字航摄资料的在西南控制困难地区外业像控的布点方案、基线数量、点位位置采取不同方案进行内业加密问题进行研究、分析,总结区域网布点方案的规律性。     

Another look at the naive estimator in a regression model

We consider the linear regression model where only a particular linear function of the dependent variables is observed, Stahlecker and Schmidt (1987) proposed a naive least squares (LS) estimator for regression coefficients in such a case. In this note we represent their estimator as a general ridge estimator. This observation leads to a view different from the previous work and provides an easy way of obtaining many important properties of the naive LS estimator. Our approach also gives some insight into the relationship between the naive LS estimator and the generalized least squares estimator.     

Forecasting levels of log variables in vector autoregressions

Sometimes forecasts of the original variable are of interest, even though a variable appears in logarithms (logs) in a system of time series. In that case, converting the forecast for the log of the variable to a naïve forecast of the original variable by simply applying the exponential transformation is not theoretically optimal. A simple expression for the optimal forecast under normality assumptions is derived. However, despite its theoretical advantages, the optimal forecast is shown to be inferior to the naïve forecast if specification and estimation uncertainty are taken into account. Hence, in practice, using the exponential of the log forecast is preferable to using the optimal forecast.     

Estimation of ratio of population means in survey sampling when some observations are missing

This paper considers the estimation of the ratio of population means when some observations are missing. Four estimators are presented and their bias and mean square error properties are studied. Received: June 1998     

Characterizations of negative multinomial distributions based on conditional distributions

In this paper characterizations of negative multinomial distributions based on conditional distributions have been studied.     

基于LMS算法的广义形态滤波器应用于转子分形故障状态识别的效果研究

将描述混沌运动的关联维数用于转子系统振动信号分析,并针对现场实测振动信号中存在噪声污染,提出了一种基于自适应形态滤波对信号进行降噪处理。该滤波器综合了不同的结构元素且在开—闭、闭—开滤波器权系数的确定上采用了基于最小均方误差算法的自适应技术,具有更好的滤波性能和细节信息保留能力;分析比较降噪前后转子4种状态(正常、油膜涡动、局部碰摩、全周碰摩)下信号的关联维数,结果表明,用含有噪声信号的关联维数描述系统的特征行为不可靠,有必要对实测信号进行降噪处理。自适应形态滤波器具有良好的降噪效果,将降噪后的关联维数作为特征量,在转子故障诊断中进行识别故障、判断运行状态具有可行性。     

A Comparison of two Robust Estimation Methods for Business Surveys

Two alternative robust estimation methods often employed by National Statistical Institutes in business surveys are two‐sided M‐estimation and one‐sided Winsorisation, which can be regarded as an approximate implementation of one‐sided M‐estimation. We review these methods and evaluate their performance in a simulation of a repeated rotating business survey based on data from the Retail Sales Inquiry conducted by the UK Office for National Statistics. One‐sided and two‐sided M‐estimation are found to have very similar performance, with a slight edge for the former for positive variables. Both methods considerably improve both level and movement estimators. Approaches for setting tuning parameters are evaluated for both methods, and this is a more important issue than the difference between the two approaches. M‐estimation works best when tuning parameters are estimated using historical data but is serviceable even when only live data is available. Confidence interval coverage is much improved by the use of a bootstrap percentile confidence interval.     

The Estimation of Pareto Distribution by a Weighted Least Square Method

The two-parameter Pareto distribution provides reasonably good fit to the distributions of income and property value, and explains many empirical phenomena. For the censored data, the two parameters are regularly estimated by the maximum likelihood estimator, which is complicated in computation process. This investigation proposes a weighted least square estimator to estimate the parameters. Such a method is comparatively concise and easy to perceive, and could be applied to either complete or truncated data. Simulation studies are conducted in this investigation to show the feasibility of the proposed method. This report will demonstrate that the weighted least square estimator gives better performance than unweighted least square estimators with simulation cases. We also illustrate that the weighted least square estimator is very close to maximum likelihood estimator with simulation studies.     

A regularization approach to the many instruments problem

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.     

Note on discrete a-unimodality

An interpretation is given of ABOUAMMOH'S (1987) discrete analogue of the (one-dimensional) definition of a-unimodality by Olshen and Savage. The concepts are of some interest in the context of selfdecomposability.     

A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.     

The locally MIMSQE of nonnormal error variance in quadratically balanced models

Without normality assumption, an explicit form of the locally minimum mean square error translation-invariant quadratic estimator for the error variance in a quadratically balanced design is obtained. The estimator depends on the kurtosis of the random error. Under the normality the estimator becomes globally optimal.     

A Note on the Newsboy Model with a Cutoff Transaction Size and Gauss Holding and Penalty Cost Functions

In recent papers, the inventory models were presented in which customers with an order larger than a prespecified cutoff transaction size are satisfied in an alternative way, against additional cost. They assumed the holding and penalty cost functions are linear functions. In this paper, the Gauss function can be applied such as the cost for mailing letters or packages in the post office. Therefore, we address a variant of the holding and penalty cost functions by considering the Gauss holding and penalty cost functions to fit in with the most practical situations. In addition, we also assume that customers with an order larger than a prespecified cutoff transaction size are still assumed to be satisfied in an alternative way. Moreover, when the maximum demand is large, much more time may be required to determine the optimal solution. Thus, we adopt and modify the algorithm of the Golden Section Search Technique to determine the optimal order-up-to level S and the cutoff transaction size q systematically and provide illustrative numerical example.     

On the Distribution of General Quadratic Functions in Normal Vectors

A representation in terms of independent standard normal variables tor the general quadratic form in normal variables in the univariate case, obtained by DIK and DE GUNST (1985), is extended to the multivariate situation. A representation for the quadratic function in normal vectors X'AX , where X is a random matrix with normally distributed elements and A a real symmetric matrix, is given in terms of independent and identically distributed central normal vectors. The representation is valid only when the covariance structure of X is of a special form, but all known results, especially necessary and sufficient conditions for X'AX to have a Wishart distribution, can easily be derived from it.     

Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.