Sample Design and Allocation for Random Digit Dialling

Sample design and sample allocation methods are developed for random digit dialling in household telephone surveys. The proposed method is based on a two-way stratification of telephone numbers. A weighted probability proportional to size sample allocation technique is used, with auxiliary variables about the telephone coverage rates, within local telephone exchanges of each substrata. This makes the sampling design nearly “self-weighting” in residential numbers when the prior information is well assigned. A computer program generates random numbers for the local areas within the existing phone capacities. A simulation study has shown greater sample allocation gain by the weighted probabilities proportional to size measures over other sample allocation methods. The amount of dialling required to obtain the sample is less than for proportional allocation. A decrease is also observed on the gain in sample allocation for some methods through the increasing sample sizes.     

Asymptotic properties of random extremes under general normalization from nonidentical distributions

In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the interrelation between the basic variables and their random size is not restricted, the limit forms as well as the sufficient conditions of convergence are derived. Moreover, when the random sample size is assumed to converge weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived.Acknowledgment. The authors are grateful to a referee for several helpful comments and for pointing out the extensive paper by Galambos (1992) leading to improvement of the representation of the paper.Received January 2002     

Gamma-Minimax Prediction for the Multinomial Distribution

Characterizations of gamma-minimax predictors for the linear combinations of the unknown parameter and the random variable having the multinomial distribution under arbitrary squared error loss are established in two situations – when the sample size is fixed and when the sample size is a realization of a random variable. It is always assumed that the available vague prior information about the unknown parameter can be described by a class of priors whose vector of first moments belongs to a suitable convex and compact set. Several known gamma-minimax and minimax results can be obtained from the characterizations derived in the present paper.     

Subjective Bayesian multivariate stratified sampling from finite populations

Summary In this paper we obtain optimum allocation formula in stratified sampling from a finite population withk characteristics under study using the superpopulation approach put forth byEricson [1969a]. Allocation at the second phase is also considered using information obtained from the first phase. Two different approaches are employed: a Bayesian posterior analysis and a Bayesian preposterior analysis. It is also shown that our allocation formulae for the second phase observations include the results ofMohd. Zubair Khan [1976] andDraper/Guttman [1968a] as special cases when the unknown characteristicX _ij possessed by the (i, j)-th element is scalar valued and the stratum sizes are large.     

Estimation under two stage random permutation models

Summary Estimation of the population mean under assumptions of non-informativeness of labels in a two stage finite population of distinguishable units has been studied. Under the random permutation model, for the two stage set up, sample mean, the natural estimator, is found to be the best.     

局部平稳性未知条件下STAR模型的线性性检验

本文讨论了局部随机游走STAR模型、局部随机趋势STAR模型的线性性检验问题,构造了Wald类检验统计量,推导出了这些统计量的极限分布,并分析了这些统计量有限样本下的统计特性;本文提出了在局部平稳性未知的条件下,进行STAR模型的线性性检验方法,构建了稳健的检验统计量。检验功效与检验水平分析表明,该统计量具有良好的检验水平及较高的检验功效。     

Optimum allocation in multivariate stratified random sampling: stochastic matrix mathematical programming

The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered, minimizing the estimated covariance matrix of estimated means subject to fixed cost or fixed total sample size. With these aims the asymptotic normality of sample covariance matrices for each strata is established. Some alternative approaches are suggested for its solution. An example is solved by applying the proposed techniques.     

Hotelling’s <Emphasis Type="Italic">T</Emphasis><Superscript>2</Superscript> control chart with two adaptive sample sizes

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T ² control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart [`(x)]{\bar{x}} chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T ² control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable.     

Optimal allocation of the sample size to strata under box constraints

In stratified random sampling without replacement boundary conditions, such as the sample sizes within strata shall not exceed the population sizes in the respective strata, have to be considered. Stenger and Gabler (Metrika, 61:137–156, 2005) have shown a solution that satisfies upper boundaries of sample fractions within the strata. However, in modern applications one may wish to guarantee also minimal sampling fractions within strata in order to allow for reasonable separate estimations. Within this paper, an optimal allocation in the Neyman-Tschuprov sense is developed which satisfies upper and lower bounds of the sample sizes within strata. Further, a stable algorithm is given which ensures optimality. The resulting sample allocation enables users to bound design weights within stratified random sampling while considering optimality in allocation.     

Allowing for uncertainty in exogenous shocks to CGE models: the case of a new renewable energy sector

The paper explores the importance of allowing for uncertainty in the magnitude of exogenous shocks in Computable General Equilibrium (CGE) models. The shock examined is the introduction of a new onshore wind sector in North East Scotland. A simple analytical model is developed to show how, a priori, the size of the new sector (the model shock) is uncertain and asymmetrically distributed as a result of spatial correlation in costs and returns across potential development locations. The importance of allowing for this uncertainty is tested by comparing the results from a CGE model where the sector size is assumed known with certainty to those from a model where the sector size is a random variable with an asymmetric distribution. The results show the extent to which allowing for uncertainty can influence the magnitude of estimated impacts with some variables more sensitive to the uncertainty than others.     

Mixed random systematic sampling designs

In this paper, an alternative sampling procedure that is a mixture of simple random sampling and systematic sampling is proposed. It results in uniform inclusion probabilities for all individual units and positive inclusion probabilities for all pairs of units. As a result, the proposed sampling procedure enables us to estimate the population mean unbiasedly using the ordinary sample mean, and to provide an unbiased estimator of its sampling variance. It is also found that the suggested sampling procedure performs well especially when the size of simple random sample is small. Received August 2001     

Model misspecification effects for biased samples

The model misspecification effects on the maximum likelihood estimator are studied when a biased sample is treated as a random one as well as when a random sample is treated as a biased one. The relation between the existence of a consistent estimator under model misspecification and the completeness of the distribution is also considered. The cases of the weight invariant distribution and the scale parameter distribution are examined and finally an example is presented to illustrate the results.     

Optimal estimates and optimal predictors of finite population characteristics in the presence of nonresponse

Summary When samples from a finite population are studied, for instance by interview, there will usually be some units from which no response is obtained. In this paper optimal predictors of finite population characteristics, when nonresponse is present, are studied. The predictors are studied under simple regression superpopulation models. The optimal predictors are connected to the classical weighted sample estimates which are shown to be maximum likelihood estimates, provided the probability function is fully described by the sampling design. The predictors are compared with respects to their efficiencies for some simple models and a possible explanation to the fact that the poststratification estimate which compensate for nonresponse does no better than the simple estimate, is pointed out.     

One-Sided Coverage Intervals for a Proportion Estimated from a Stratified Simple Random Sample

Using an Edgeworth expansion to speed up the asymptotics, we develop one-sided coverage intervals for a proportion based on a stratified simple random sample. To this end, we assume the values of the population units are generated from independent random variables with a common mean within each stratum. These stratum means, in turn, may either be free to vary or are assumed to be equal. The more general assumption is equivalent to a model-free randomization-based framework when finite population correction is ignored. Unlike when an Edgeworth expansion is used to construct one-sided intervals under simple random sampling, it is necessary to estimate the variance of the estimator for the population proportion when the stratum means are allowed to differ. As a result, there may be accuracy gains from replacing the normal  z -score in the Edgeworth expansion with a  t -score.     

Stock market volatility forecasting: Do we need high-frequency data?

The general consensus in the volatility forecasting literature is that high-frequency volatility models outperform low-frequency volatility models. However, such a conclusion is reached when low-frequency volatility models are estimated from daily returns. Instead, we study this question considering daily, low-frequency volatility estimators based on open, high, low, and close daily prices. Our data sample consists of 18 stock market indices. We find that high-frequency volatility models tend to outperform low-frequency volatility models only for short-term forecasts. As the forecast horizon increases (up to one month), the difference in forecast accuracy becomes statistically indistinguishable for most market indices. To evaluate the practical implications of our results, we study a simple asset allocation problem. The results reveal that asset allocation based on high-frequency volatility model forecasts does not outperform asset allocation based on low-frequency volatility model forecasts.     

Optimizing the spatial assignment of schools to reduce both inequality of educational opportunity and potential opposition rate through introducing random mechanism into proximity-based system

A serious spatial inequality of educational opportunity was revealed worldwide, for wealthy families can access good schools by buying real estate with good school' enrollment quota. Although the existing studies had revealed that random-based school assignment can significantly improve equality of opportunity allocation, random mechanism was adopted only in few places. Two major resistances of introducing random mechanism exist: the possibility of increased commuting distance to schools and the effected relative beneficiaries. In order to make the random-based allocation more feasible, this study proposes a spatial optimization model to take these two factors into account into proximity-based school assignment system. The proposed multi-objective allocation model, with the constraint conditions of assigning students to 3 closest schools and school capacities, was developed in this study to minimize the spatial disparity of educational opportunity and the potential opposition rate of introducing random mechanism into proximity-based assignment system. The model will be solved by a heuristic algorithm and applied to a case study area of Shijingshan District, Beijing. The results showed that the proposed model could improve spatial equality of educational opportunity significantly, but along with a minor increase on commuting distance to schools. In addition, potential opponents of introducing random mechanism decrease as the weight of parameters related to opposition rate increases in the model, reducing nearly 10% in the best case. Therefore, the solutions provided by proposed model may encounter less resistance in a democratic voting system. However, the results also indicated that there would be some relative beneficiaries who may oppose introducing random mechanism into proximity-based school system even in the best case. This implies that, to achieve equal educational opportunity in the context of proximity-based school system, optimized allocation is needed along with a more even distribution of educational resources.     

Optimum strategies for estimating the variance of a finite population under a superpopulation model

Considering a superpopulation model we have derived optimum model-unbiased, design-unbiased and model-design unbiased strategies for estimating the variance of a finite population. Bayesian estimation of variance w.r.t. priors covered by this model has also been looked into and some of its properties investigated.     

The system of towns with spatial public goods

In this paper, we introduce a model of ‘spatial public goods’, whose provision costs depend on the size of the benefit area. It is assumed that there are many developers providing spatial public goods in their towns. Each developer chooses the area size of his/her town and the quality of its spatial public good so as to maximize profit, taking the market price system as given. Each consumer chooses the level of the public good, and hence the town that supplies it, so as to maximize his/her utility. We show that the competitive equilibrium allocation of this economy is efficient.     

Optimum allocation in stratified sampling with replacement

In a stratified sample, when sampling is done with replacement in each stratum a better estimate of the population mean can be achieved by considering the distinct units only. An explicit expression for the variance for the mean, of a stratified sample based on the distinct units only, is obtained. Then the optimum allocation for the different stratum are obtained by minimizing this variance subject to (i) total sample size being fixed, or (ii) the expected number of distinct units being fixed. Neyman’s solutions are obtained as special cases. The solutions finally arrived at are algebraically complex, hence, numerical methods are applied. In all examples, the variance of the estimates obtained by this method are smaller than the variances obtained by Neyman’s allocation. A part of this work was supported by the Office of the Ordinance Research; U.S.A. Grant (DA-AROL(D)-31-124-G83) when the author was at University of California, Berkeley.