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Journal ArticleDOI

The Horvitz-Thompson Theorem as a Unifying Perspective for Probability Sampling: With Examples from Natural Resource Sampling

01 Aug 1995-The American Statistician (Taylor & Francis Group)-Vol. 49, Iss: 3, pp 261-268
TL;DR: The Horvitz-Thompson theorem as mentioned in this paper offers a needed integrating perspective for teaching the methods and fundamental concepts of probability sampling, and helps to avoid some common stumbling blocks of beginning students.
Abstract: Courses in sampling often lack a coherent structure because many related sampling designs, estimators, variances, and variance estimators are presented as separate cases. The Horvitz-Thompson theorem offers a needed integrating perspective for teaching the methods and fundamental concepts of probability sampling. Development of basic concepts in sampling via this approach provides the student with tools to solve more complicated problems, and helps to avoid some common stumbling blocks of beginning students. Examples from natural resource sampling are provided to illustrate applications and insight gained from this approach.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors use point processes or marked point processes (PPP) to model the characteristics of a single-tree forest, where the points are tree locations and the marks are tree characteristics such as diameter at breast height or degree of damage by environmental factors.
Abstract: Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the "points" are tree locations and the "marks" are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point pro- cess characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for under- standing and quantifying ecological relationships. Models of point pro- cesses are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest structures and for the prediction of results of forestry operations such as plantation and thinning.

498 citations

Journal ArticleDOI
TL;DR: The current status of accuracy assessment that has emerged from nearly 50 years of practice is described and improved methods are required to address new challenges created by advanced technology that has expanded the capacity to map land cover extensively in space and intensively in time.

276 citations

Journal ArticleDOI
TL;DR: The papers in this special section on Bayesian statistics exemplify thedifficulties inherent in making convincing scientific arguments with Bayesian reasoning.
Abstract: Bayesian statistics involve substantial changes in the methods and philos- ophy of science. Before adopting Bayesian approaches, ecologists should consider carefully whether or not scientific understanding will be enhanced. Frequentist statistical methods, while imperfect, have made an unquestioned contribution to scientific progress and are a workhorse of day-to-day research. Bayesian statistics, by contrast, have a largely untested track record. The papers in this special section on Bayesian statistics exemplify the diffi- culties inherent in making convincing scientific arguments with Bayesian reasoning.

212 citations

Journal ArticleDOI
TL;DR: A population-based statistical framework is developed to examine how the spatial unit chosen affects the outcome of an accuracy assessment and how the population, values of the accuracy parameters, and sampling design are impacted by the choice of spatial unit.

139 citations

Journal ArticleDOI
TL;DR: A limit theorem for estimators of a general, possibly infinite dimensional parameter based on unbiased estimating equations containing estimated nuisance parameters is state and proved.
Abstract: . We consider semiparametric models for which solution of Horvitz–Thompson or inverse probability weighted (IPW) likelihood equations with two-phase stratified samples leads to consistent and asymptotically Gaussian estimators of both Euclidean and non-parametric parameters. For Bernoulli (independent and identically distributed) sampling, standard theory shows that the Euclidean parameter estimator is asymptotically linear in the IPW influence function. By proving weak convergence of the IPW empirical process, and borrowing results on weighted bootstrap empirical processes, we derive a parallel asymptotic expansion for finite population stratified sampling. Several of our key results have been derived already for Cox regression with stratified case–cohort and more general survey designs. This paper is intended to help interpret this previous work and to pave the way towards a general Horvitz–Thompson approach to semiparametric inference with data from complex probability samples.

137 citations


Cites background from "The Horvitz-Thompson Theorem as a U..."

  • ...…for a very general class of designs in terms of the first- and second-order inclusion probabilities: i the probability of including the ith of N phase 1 observations in the phase 2 sample, and ii′ the probability that the observations labelled i and i′ are both included (Overton & Stehman, 1995)....

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References
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Journal ArticleDOI
TL;DR: In this paper, two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable, which is a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used.
Abstract: This paper presents a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used. Two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable. Admittedly, these two schemes have limited application. They should prove useful, however, for the first stage of sampling with multi-stage designs, since both permit unbiased estimation of the sampling variance without resorting to additional assumptions. * Journal Paper No. J2139 of the Iowa Agricultural Experiment Station, Ames, Iowa, Project 1005. Presented to the Institute of Mathematical Statistics, March 17, 1951.

3,990 citations


"The Horvitz-Thompson Theorem as a U..." refers background or methods in this paper

  • ...The Horvitz-Thompson theorem may be used to derive estimators and variances for many commonly used designs (Horvitz and Thompson 1952; Overton and Stehman 1992; SSW 1992)....

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  • ...Other examples are presented by Horvitz and Thompson (1952) and SSW (1992)....

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  • ...However, the Horvitz-Thompson theorem (Horvitz and Thompson 1952) has much greater theoretical importance and practical utility than these restricted treatments demonstrate, as it provides a unifying generalization for a large part of design-based sampling....

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Book
22 May 1997
TL;DR: This book presents the principles of Estimation for Finite Populations and Important Sampling Designs and a Broader View of Errors in Surveys: Nonsampling Errors and Extensions of Probability Sampling Theory.
Abstract: PART I: Principles of Estimation for Finite Populations and Important Sampling Designs: Survey Sampling in Theory and Practice. Basic Ideas in Estimation from Probability Samples. Unbiased Estimation for Element Sampling Designs. Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages. Introduction to More Complex Estimation Problems.- PART II: Estimation through Linear Modeling, Using Auxiliary Variables: The Regression Estimator. Regression Estimators for Element Sampling Designs. Regression Estimators for Cluster Sampling and Two-Stage Sampling.- PART III: Further Questions in Design and Analysis of Surveys: Two-Phase Sampling. Estimation for Domains. Variance Estimation. Searching for Optimal Sampling Designs. Further Statistical Techniques for Survey Data.- PART IV: A Broader View of Errors in Surveys: Nonsampling Errors and Extensions of Probability Sampling Theory. Nonresponse. Measurement Errors. Quality Declarations for Survey Data.- Appendix A - D.- References.

3,197 citations

Book
01 Jan 1987
TL;DR: In this paper, the authors proposed three-stage sampling: simple random sampling, two stage sampling and three stage sampling, and two-stage and double sampling, respectively, to estimate the mean and variance from censored data sets.
Abstract: Sampling Environmental Populations. Environmental Sampling Design. Simple Random Sampling. Stratified Random Sampling. Two-Stage Sampling. Compositing and Three-Stage Sampling. Systematic Sampling. Double Sampling. Locating Hot Spots. Quantiles, Proportions, and Means. Skewed Distributions and Goodness-of-Fit Tests. Characterizing Lognormal Populations. Estimating the Mean and Variance from Censored Data Sets. Outlier Detection and Control Charts. Detecting and Estimating Trends. Trends and Seasonality. Comparing Populations. Appendices. Symbols. Glossary. Bibliography. Index.

2,253 citations

Book
01 Jun 1973

1,288 citations

Book
13 Dec 1990
TL;DR: In this paper, a description of variable material sampling and estimation generalization, prediction, and classification relations between variables, covariance and correlation regression relations between individuals, similarity ordination analysis of dispersion and discrimination numerical classification, hierarchical systems numerical classification - non hierarchical methods spatial dependence nested sampling and analysis local estimation, kriging.
Abstract: Quantitative description of variable material sampling and estimation generalization, prediction, and classification relations between variables - covariance and correlation regression relations between individuals - similarity ordination analysis of dispersion and discrimination numerical classification - hierarchical systems numerical classification - non hierarchical methods spatial dependence nested sampling and analysis local estimation - kriging.

775 citations