Randomized response: Estimating mean square errors of linear estimators and finding optimal unbiased strategies

Summary General procedures are described to generate quantitative randomized response (RR) required to estimate the finite population total of a sensitive variable. Permitting sample selection with arbitrary probabilities a formula for the mean square error (MSE) of a linear estimator of total based on RR is noted indicating the simple modification over one that might be based on direct response (DR) if the latter were available. A general formula for an unbiased estimator of the MSE is presented. A simple approximation is proposed in case the RR ratio estimator is employed based on a simple random sample (SRS) taken without replacement (WOR). Among sampling strategies employing unbiased but not necessarily linear estimators based on RR, certain optimal ones are identified under two alternative models analogously to well-known counterparts based on DR, if available. Unlike Warner’s (1965) treatment of categorical RR we consider quantitative RR here.     

Relative efficiency and deficiency of kernel type estimators of smooth distribution functions

Abstract  The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.     

On two properties of an unequal probability sampling scheme

Summary For an inclusion probability proportional to size (IPPS) sampling scheme recently proposed by Saxena, Singh and Srivastava (1986), it is shown that under certain simple verifiable conditions (1) the Horvitz-Thompson (1952) estimator based on it has a smaller variance than the variance of the Hansen-Hurwitz (1943) estimator based on probability proportional to size (PPS) sampling with replacement (WR) both involving the same size-measures and the expected sample size in the former being equal to the number of draws in the latter and (2) the Yates-Grundy (1953) estimator for the variance of the Horvitz-Thompson estimator based on this IPPS scheme is uniformly non-negative.     

Asymptotic second-order efficiency of three-stage procedure with a warranted confidence level

This paper considers a three-stage procedure which was proposed by Holm (1995) to yield a fixed-width confidence interval of the normal mean with a precise confidence level. The procedure is shown to be asymptotically second-order efficient. The procedure is also applied to such problems as bounded risk and hypothesis testing     

Robust estimation for the order of finite mixture models

In this paper, we study a robust and efficient estimation procedure for the order of finite mixture models based on the minimizing a penalized density power divergence estimator. For this task, we use the locally conic parametrization approach developed by Dacunha-Castelle and Gassiate (ESAIM Probab Stat 285–317, 1997a; Ann Stat 27:1178–1209, 1999), and verify that the minimizing a penalized density power divergence estimator is consistent. Simulation results are provided for illustration.     

On the application of the Minkowski-Farkas theorem to sampling designs

In the paper, we consider the following problem: Let {π_k} be a sequence satisfying 0π_kΣ1 (k=1,…, N) and π=n.Tben, is there an unordered sampling design such that, for each k=1,…N, the inclusion probability of unit k is equal to π? It is shown that it can be solved by the straightforward application of the Minkowski-Farkas theorem.     

浅谈沥青路面施工质量动态控制

对沥青路面施工质量的动态控制理论与方法进行了介绍,针对动态控制过程的关键指标的选取,权重的分配,取样方法的研究进行了重点的阐述,得到的结论在今后开展沥青路面施工质量动态控制中有一定的参考意义。     

Estimating the Size of the Homeless Population in Budapest,Hungary

In this study we try to estimate the size of the homeless population in Budapest by using two – non-standard – sampling methods: snowball sampling and capture-recapture method. Using two methods and three different data sets we are able to compare the methods as well as the results, and we also suggest some further applications. Apart from the practical purpose of our study there is a methodological one as well: to use two relatively unknown methods for the estimations of this very peculiar kind of population.     

从产业结构效率论产业结构调整方向——以秦皇岛市为例

通过对秦皇岛市三次产业结构现状及效率的多角度分析,指出现阶段第二产业发育不足是制约秦皇岛市整体经济发展水平的关键因素,加快工业发展应成为该地区今后产业结构调整的主要方向。     

Estimation of a survival curve with randomly censored data in the presence of a covariate

This paper deals with the estimation of a survival curve in models with random right censoring and dependent censoring mechanism. We consider a specific dependent censorship model in which conditional on a covariate, the survival and censoring times are assumed to be independent. We investigate asymptotic properties of a corrected version of a survival curve estimator introduced by Cheng (1989). In particular we show uniform strong consistency and weak convergence to a Gaussian process. Comparisons of this estimator with the well-known Kaplan-Meier-estimator are included. Finally, some examples illustrate how the estimator performs. Received: February 2000     

论火电厂锅炉给粉机不同运行方式对锅炉燃烧效率的影响

对大型火力发电厂而言,锅炉燃烧效率的高低直接影响到整个机组的经济性。文章通过实验,探讨了锅炉给粉机在不同运行方式下对锅炉效率的影响,从而指导我们在日常运行中优化给粉机配置,提高锅炉燃烧效率。     

浅析输电线路不停电跨越架线施工技术

随着经济的发展,电力行业发展越来越快,输电线路因此不断增加。目前,我国输电线路面临着新建线路与带电线路交叉跨越的现状,如果某地区需要申请停电,停电施工会非常复杂,即使满足了停电需求,施工也要等待很长一段时间,从而影响整个电网工程建设。为了解决这一难题,不停电跨越施工技术应运而生,因此,研究人员必须对输电线路不停电跨越架线施工技术进行分析和总结。笔者结合多年工作经验,从不停电跨越架线施工的一般方法和流程着手,对输电线路不停电跨越架线施工技术作了简要分析。     

浅谈如何提高ZC3500装车机效率

码头散货装载流程中,装车机是整个散装系统的重要组成部分,作为物料装载的终端设备,装车机的工作效率往往决定着装货流程乃至整个散货现场的作业效率,文中分析了影响ZC3500型装车机工作效率的一些因素,在此基础上提出了相关措施,对提高码头装车系统的工作效率有着重要意义。     

Estimating banking cost efficiency with the consideration of cost management

This study re-investigates the bank cost efficiency by a combination of two strands of literature. The first strand is related to bank cost efficiency; the other is related to earnings management. Employing the findings reported in bank earnings management literature, this study argues that bank observed total cost (“accounting cost”) may be the biased estimator of the true total cost. Using the biased total cost may thus yield incorrect inferences from estimating bank cost efficiency. We propose a method to modify accounting cost, which is referred to as “economic cost”, to be consistent with the economic theory; that is, one that is free of cost management. Both accounting and economic costs are then adopted to analyze the efficiency of 29 commercial banks in Taiwan banking industry. Our results show that estimated efficiency, with the application of economic cost, offers results that are more reasonable results than those of the accounting cost.     

On the Conditional Variance of Fuzzy Random Variables

The conditional variance of random variables plays an important role for well-known variance decomposition formulas. In this paper, the conditional variance is defined for fuzzy random variables and some properties are proved, which especially generalize to the mentioned variance decomposition. Moreover, results for two special types of fuzzy random variables and an outlook for possible applications are presented.     

A stochastic frontier analysis to estimate the relative efficiency of Spanish airports

There exists a common belief among researchers and regional policy makers that the actual central system of Aeropuertos Españoles y Navegación Aérea (AENA) should be changed to one more decentralized where airport managers could have more autonomy. The main objective of this article is to evaluate the efficiency of the Spanish airports using Markov chain Monte Carlo (MCMC) simulation to estimate a stochastic frontier analysis (SFA) model. Our results show the existence of a significant level of inefficiency in airport operations. Additionally, we provide efficient marginal cost estimates for each airport which also cast some doubts about the current pricing practices.     

土石坝无基坑筑坝施工技术研究

在河床上修建土石坝,一般先要修筑施工围堰,然后进行基坑抽水和开挖,再进行坝基防渗处理和度汛堰体的填筑。传统的施工方法,在前期围堰、挖掘基坑的环节,需要占用河床枯水期较多时间,这样就导致后期的坝基防渗处理和度汛坝体填筑的工期十分紧张,如果遇上汛期较早的年份,就会给施工带来很大困难。在这种情况下,探索新的筑坝技术显得很有必要。本文就是通过对无基坑施工技术的现状、可行性和关键技术进行研究分析,从而得出无基坑施工技术将在未来的筑坝技术中有广阔的应用前景。     

On the Ratio of Fréchet Random Variables

The distribution of the ratio X/Y is derived when X and Y are independent Fréchet random variables. Extensive tabulations of the associated percentage points are also given.     

On the distribution of estimated technical efficiency in stochastic frontier models

We consider a stochastic frontier model with error ε=v−u$\epsilon =v-u$, where v$v$ is normal and u$u$ is half normal. We derive the distribution of the usual estimate of u,E(u|ε)$u,E\left(u\right|\epsilon )$. We show that as the variance of v$v$ approaches zero, E(u|ε)−u$E\left(u\right|\epsilon )-u$ converges to zero, while as the variance of v$v$ approaches infinity, E(u|ε)$E\left(u\right|\epsilon )$ converges to E(u)$E\left(u\right)$. We graph the density of E(u|ε)$E\left(u\right|\epsilon )$ for intermediate cases. To show that E(u|ε)$E\left(u\right|\epsilon )$ is a shrinkage of u towards its mean, we derive and graph the distribution of E(u|ε)$E\left(u\right|\epsilon )$ conditional on u$u$. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting.     

On Estimators of the Nearest Neighbour Distance Distribution Function for Stationary Point Processes

There are three approaches for the estimation of the distribution function D(r) of distance to the nearest neighbour of a stationary point process: the border method, the Hanisch method and the Kaplan-Meier approach. The corresponding estimators and some modifications are compared with respect to bias and mean squared error (mse). Simulations for Poisson, cluster and hard-core processes show that the classical border estimator has good properties; still better is the Hanisch estimator. Typically, mse depends on r, having small values for small and large r and a maximum in between. The mse is not reduced if the exact intensity λ (if known) or intensity estimators from larger windows are built in the estimators of D(r); in contrast, the intensity estimator should have the same precision as that of λ D(r). In the case of replicated estimation from more than one window the best way of pooling the subwindow estimates is averaging by weights which are proportional to squared point numbers.