Author

# M. P. Singh

Bio: M. P. Singh is an academic researcher. The author has contributed to research in topics: Statistical model & Estimator. The author has an hindex of 1, co-authored 1 publications receiving 49 citations.

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01 Jan 1988

TL;DR: In this paper, the authors present a unified theory of sampling and a set of strategies for survey sampling, including the Horvitz-Thompson Estimator (HETE) and the Bayesian approach.

Abstract: Part A: Unified Theory of Sampling. Introduction. Principal Notation and Formulation of the Main Problem. Design-Based Estimation. Admissibility and Other Optimality Properties of Sampling Designs. Sufficiency and Related Concepts in Survey Sampling. Sample Survey and General Statistical Model. Further Details on Likelihood and Bayesian Approach. Predictive Approach. Robustness. Concluding Remarks. Appendices: An Optimality Property of the Sample Mean. Alternative Models and Relative Performances of Sampling Strategies. Inference About Symmetric Functions of Exchangeable Populations: Non-Informativeness of Labels. Robustness of Strategies. Part B: Strategies of Sampling. Introduction and Summary. The Horvitz-Thompson Estimator. Subdivision of Sampling Schemes. Sampling Schemes for Use of the HTE: n=2. Sampling Schemes for Use of the HTE: General n. Sampling with Other Strategies. Alternative Estimators. Ratio, Product, and Regression Estimators. Variance Estimation. Special Designs. Comparison of Strategies. Appendices: Varying Probability Sampling for Robust Estimation. Optimality of HTE Under Random Permutation Labelling. References.

49 citations

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TL;DR: In this article, the authors describe sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit, if any of these additional units satisfies the condition, still more units may be added.

Abstract: In many real-world sampling situations, researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting. This article describes sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit. If any of these additional units satisfies the condition, still more units may be added. Sampling designs such as these, in which the selection procedure is allowed to depend on observed values of the variable of interest, are in contrast to conventional designs, in which the entire selection of units to be included in the sample may be determined prior to making any observations. Because the adaptive selection procedure introduces biases into conventional estimators, several estimators are given that are design unbiased for the population mean with the adaptive cluster designs of this article; that is, the ...

420 citations

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TL;DR: In this paper, a quadratic zero-one model is formulated for diversity maximization and two equivalent linear integer programs are then presented that offer progressively greater computational efficiency, and an example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.

Abstract: The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero-one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP-hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.

164 citations

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TL;DR: In this article, the authors present two methods for stepwise selection of sampling units, and corresponding schemes for removal of units that can be used in connection with sample rotation, and describe practical, geometrically convergent algorithms for computing the wi from the 7i.

Abstract: SUMMARY Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities 7Ci, or equivalently as having the probability of a selected sample proportional to the product of a set of 'weights' wi. We show the essential uniqueness of the wi given the 7i, and describe practical, geometrically convergent algorithms for computing the wi from the 7i. We present two methods for stepwise selection of sampling units, and corresponding schemes for removal of units that can be used in connection with sample rotation. Inclusion probabilities of any order can be written explicitly in closed form. Second-order inclusion probabilities 7rij satisfy the condition 0< ij < 7ic 7j, which guarantees Yates & Grundy's variance estimator to be unbiased, definable for all samples and always nonnegative for any sample size.

158 citations

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TL;DR: In this article, the authors compare the assumptions and use of classical sampling theory with those of geostatistical theory, and conclude that this view is both false and unfortunate, and that estimates of spatial means based on classical sampling designs require fewer assumptions for their validity.

Abstract: A commonly held view among geostatisticians is that classical sampling theory is inapplicable to spatial sampling because spatial data are dependent, whereas classical sampling theory requires them to be independent. By comparing the assumptions and use of classical sampling theory with those of geostatistical theory, we conclude that this view is both false and unfortunate. In particular, estimates of spatial means based on classical sampling designs require fewer assumptions for their validity, and are therefore more robust, than those based on a geostatistical model.

155 citations

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TL;DR: In this article, a modification of the adaptive cluster design is introduced, in which networks are sampled only once, and two unbiased estimators are considered and the Rao-Blackwell theorem is used to improve them in terms of efficiency.

Abstract: SUMMARY In the adaptive cluster design introduced by Thompson (1990), a finite population of units under investigation is partitioned into networks on the basis of a specified condition for adding neighbourhoods to a sampled unit. An initial sample of units is taken and a network may be sampled more than once. In this paper, we introduce a modification of the design in which networks are sampled only once. Two unbiased estimators are considered and the Rao-Blackwell theorem is used to improve them in terms of efficiency. The various estimators are compared using two examples.

46 citations