On a pragmatic modification of survey sampling in three stages

Presented are formulae for an unbiased estimator of a finite population total and an unbiased variance estimator for it when samples are taken by usual procedures in the first two stages with varying probabilities but the third stage units are sampled for economy and convenience in a non-standard way from the pool of all sampled second stage units rather than independently from each of the latter separately containing the former.     

A Variance Estimator for Systematic Sampling from a Deliberately Ordered Population

ABSTRACT

The systematic sampling (SYS) design (Madow and Madow, 1944 Madow , L. H. , Madow , W. G. ( 1944 ). On the theory of systematic sampling . Ann. Math. Statist. 15 : 1 – 24 .[Crossref] , [Google Scholar]) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]) and usual variance estimators (Yates and Grundy, 1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Roy. Statist. Soc. Series B 1 : 253 – 261 . [Google Scholar]) are inadequate and can overestimate the variance significantly (Särndal et al., 1992 Särndal , C. E. , Swenson , B. , Wretman , J. H. ( 1992 ). Model Assisted Survey Sampling . New York : Springer-Verlag , Ch. 3 .[Crossref] , [Google Scholar]). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.     

Heterogeneity,Aggregate Uncertainty,and the Short-Term Interest Rate

This article analyzes the relationship between the short-term interest rate and diversity (i.e., the number of types) in models with heterogeneous agents and incomplete markets. The number of types needed to approximate a continuum varies across examples. In all cases, however, the number of types has little effect on the average interest rate and consumption variability. In these models, the set of state variables is large because the equilibrium law of motion depends on the cross-sectional wealth distribution. The article shows how to solve these models numerically by approximating the distribution using moments or percentiles.     

Shrinkage of Variance for Minimum Distance Based Tests

This paper promotes information theoretic inference in the context of minimum distance estimation. Various score test statistics differ only through the embedded estimator of the variance of estimating functions. We resort to implied probabilities provided by the constrained maximization of generalized entropy to get a more accurate variance estimator under the null. We document, both by theoretical higher order expansions and by Monte-Carlo evidence, that our improved score tests have better finite-sample size properties. The competitiveness of our non-simulation based method with respect to bootstrap is confirmed in the example of inference on covariance structures previously studied by Horowitz (1998 Horowitz , J. ( 1998 ). Bootstrap methods for covariance structures . The Journal of Human Resources 33 : 39 – 61 .[Crossref], [Web of Science ®] , [Google Scholar]).     

程序价值论

程序价值和程序的效能价值是程序的价值的构成。强调后者忽视前者是当前程序的价值观存在的问题。划清程序价值和程序的效能价值的界限,明晰程序价值的内涵及程序价值的内在偏差,有利于还程序价值应有的地位;而要真正实现程序价值,就必须寻求协调其内在偏差的方式和途径、建立有效的保障机制。     

Moderate deviations for the moment estimators in Rayleigh distribution with two parameters

ABSTRACT

We study the moderate deviations of the moment estimators in Rayleigh distribution with two parameters. The moderate deviations are obtained by the delta method in large deviation principle.     

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE

Statistics as data is ancient, but as a discipline of study and research it has a short history. Courses leading to degrees in statistics have been introduced in universities some sixty to seventy years ago. They were not considered to constitute a basic discipline with a subject matter of its own. However, during the last seventy five years, it has developed as a powerful blend of science, technology and art for solving problems in all areas of human endeavor. Now-a-days statistics is used in scientific research, economic development through optimum use of resources, increasing industrial productivity, medical diagnosis, legal practice, disputed authorship, and optimum decision making at individual and institutional levels. What is the future of statistics in the coming millennium dominated by information technology encompassing the whole of communications, interaction with intelligent systems, massive data bases, and complex information processing networks? The current statistical methodology based on probabilistic models applied on small data sets appears to be inadequate to meet the needs of the society in terms of quick processing of data and making the information available for practical purposes. Adhoc methods are being put forward under the title Data Mining by computer scientists and engineers to meet the needs of customers. The paper reviews the current state of the art in statistics and discusses possible future developments considering the availability of large data sets, enormous computing power and efficient optimization techniques using genetic algorithms and neural networks.

     

SOME SIMPLE APPROXIMATIONS FOR THE DOUBLY NONCENTRAL z DISTRIBUTION

We give two simple approximations for evaluating the cumulative probabilities of the doubly noncentral z distribution. These can easily be used for evaluating the cumulative probabilities of the doubly noncentral F distribution as well. We compare our results with those obtained by Tiku (1965) using series expansion. An industrial situation where a quality characteristic of interest follows the doubly noncentral z distribution is also cited. However, in this case the exact probabilities could be calculated using results on the ratio of two normal variables.     

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Abstract.  Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size π ps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance–rejection filter. A new very efficient method to generate conditional Poisson ( CP ) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz–Thompson estimator.