Solutions to the Problem of Unequal Probability Sampling without Replacement

Sunter, A. B.

doi:10.2307/1403257

Cited by 21 publications

(8 citation statements)

References 3 publications

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“…Example 6 (Generalized Sunter method). Sunter's (1986) method is a list sequential procedure for obtaining a πps sample of fixed size n. The units of U are successively gone through in the order 1, 2, . .…”

Section: Different Applications Of the Splitting Methodsmentioning

confidence: 99%

The Splitting Method for Unequal Probability Sampling

Bondesson¹

2014

Wiley StatsRef: Statistics Reference Online

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Section: Different Applications Of the Splitting Methodsmentioning

confidence: 99%

The Splitting Method for Unequal Probability Sampling

Bondesson¹

2014

Wiley StatsRef: Statistics Reference Online

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“…An ideal ordering would be close to the requirements of Corollary 1.1 in Sunter (1986) which states: if N x N-n t + l =x N-n t + 2 = ---=x N> n t x i <X i = .£ x j with i = j = 1 1, 2, N-n t for some ordering of the population, then x* = 0 will work. Then a sample of exactly n t units will be obtained.…”

Section: Review Of Literaturementioning

confidence: 97%

“…As Sunter (1986) indicates, under any set of positive selection probabilities, a Horvitz-Thompson estimator N of the population total Y = L Y i is given by Y = .^Yi/IIi [1] where n a is the achieved sample size, with variance VfY) =.E i Y i 2(i-n i )/n i -E ¥^(^11,-11^/114111 and unbiased variance estimator (if Ely > 0 for all i,j) v(Y)^E^il-U^-'L Y^U^-U^/U^U^ [ 2] For fixed n,:…”

Section: Review Of Literaturementioning

confidence: 99%

Sunter's pps without replacement sampling as an alternative to Poisson sampling /

Schreuder¹,

Li²,

Sadooghi-Alvandi³

et al. 1990

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An alternative to Poisson sampling called Sunter sampling is introduced into the forestry literature. The probability of selecting a sample unit depends on its size and the number of previous units selected as well as on the sizes and number of units remaining in the population. This results in a less variable sample size than in Poisson sampling. Sunter sampling is more efficient than Poisson sampling where a sampling list is available prior to sampling if a slightly biased adjusted estimator similar to one in Poisson sampling is used. Approximate true variances are given for both the unadjusted and adjusted estimators. Two sample-based variance approximations provide reliable estimates of both the true and simulation variance of the adjusted estimator. Sunter sampling is not yet a practical alternative when no sampling list is available but perhaps could be an alternative to, for example, point-Poisson sampling.A new sampling scheme is introduced that could be quite efficient in timber sales and other inventories. Some of these inventories currently suffer from random sample sizes which may result in inventories being more costly or less precise than planned for. The study suggests applications where this new method may be useful.

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“…This design will be denoted ~p x , for "inclusion probability proportional to x." Variable probability systematic (VPS) sampling is one of the most easily implemented, fixed sample size ~p x designs (Sunter 1986). Two VPS designs are distinguished.…”

Section: Statistical Settingmentioning

confidence: 99%

Comparison of Variance Estimators of the Horvitz-Thompson Estimator for Randomized Variable Probability Systematic Sampling

Stehman

Overton

1994

Journal of the American Statistical Association

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The National Stream Survey (NSS) and Environmental Monitoring and Assessment Program (EMAP) use variable probability, systematic sampling, and the Horvitz-Thompson estimator to estimate population parameters of ecological interest. A common strategy of variance estimation for systematic sampling is to assume that the population order had been randomized prior to sampling and to estimate variance under this randomized population model. The Yates-Grundy variance estimator is generally recommended for estimating the variance of the Horvitz-Thompson estimator under this model. But design features of NSS and EMAP preclude application of the Yates-Grundy estimator, so use of the Horvitz-Thompson variance estimator is required. Further, because the first-order inclusion probabilities are known only for the sample units and not the entire population, neither the actual pairwise inclusion probabilities ( ruv's) nor the Hartley-Rao approximation of the r,'s can be computed. Thus the variance estimator proposed for use in these surveys was the Horvitz-Thompson variance estimator computed with a new approximation to the r,'s. Having to use this estimator, denoted motivated exploration of the general question of when behaviors of the Horvitz-Thompson andYates-Grundy variance estimators differ and also investigation ofthe specific performance of the estimator t)gT. To permit comparison of variance estimators, we restricted attention to fixed sample size, variable probability systematic sampling, from a randomly sorted list. Properties of uGT were compared to those of three other variance estimators: the Yates-Grundy estimator calculated with both the new ruu approximation and the Hartley-Rao approximation, and the Horvitz-Thompson variance estimator calculated with the Hartley-Rao approximation. An empirical study, designed to permit generalization beyond a few special case populations, demonstrated that superiority of the Yates-Grundy variance estimator was restricted to populations having both high correlation between the response variable, y , and the selection variable, x , and approximately equal coefficients of variation for the x and y populations.With the exception of these populations, uGT performed nearly the same as the Yates-Grundy estimators studied and performed better than the Horvitz-Thompson variance estimator computed with the Hartley-Rao approximation. In NSS and EMAP most response variables are not expected to be highly correlated with the selection variable, so wGT should furnish an adequate variance approximation when the randomized population model holds.

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Solutions to the Problem of Unequal Probability Sampling without Replacement

Cited by 21 publications

References 3 publications

The Splitting Method for Unequal Probability Sampling

The Splitting Method for Unequal Probability Sampling

Sunter's pps without replacement sampling as an alternative to Poisson sampling /

Comparison of Variance Estimators of the Horvitz-Thompson Estimator for Randomized Variable Probability Systematic Sampling

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