PPS Sampling Research Articles

Probability proportional to size (πps) sampling using ranks

There can be gains in estimation efficiency over equal probability samplin methods when one makes use of auxiliary information for probability proporti onal to size with replacement (πpswr) sampling methods. The usual method is simple to execute, but might lead to more than one appearance in the sampl e for any particular unit. When a suitable variable x is not available, one may know how to rank units reasonably well relative to the unknown y values before sample selection. When such ranking is possible, we introduce a simple and efficient sampling plan using the ranks as the unknown x measures of size. The proposed sampling plan is similar to, has the simplicity of, and has no greater sampling variance than with replacement sampling, but is without replacement.

Efficiency of a new estimator in PPS sampling for multiple characteristics

Abstract Bansal and Singh (1985) have developed an alternative estimator for the probability proportional to size with replacement sampling scheme when certain characteristics under study are poorly correlated with the selection probabilities. We suggest, in this paper, a more intuitive and meaningful estimator and study its efficiency compared with other related estimators.

General diseases and dental treatability of the institutionalized elderly Finnish population.

The purpose of the present study was to investigate the relationship between such general diseases and dental treatability of the elderly living in municipal old people's homes in Finland. The sampling methods used were PPS sampling (probabilities proportionate to size), and non-randomized and randomized sampling. The subjects were 480 residents of 24 municipal old people's homes in different parts of Finland. Of the subjects 153 were men and 327 women, and their ages ranged from 65 to 100 yr. Data on the general diseases was obtained from the subjects' medical histories. The assessment of dental treatability was based on the subjects' communicative ability and cooperation during interview, on a clinical oral examination, and on the subjects' ability to cope with the stress of an interview and examination. Eleven percent of the subjects had no diagnosed diseases, whereas 28% had three or more. The most common diseases in both men and women were cardiovascular diseases followed by respiratory disorders in men and endocrine disorders in women. The dental treatability was considered very poor or poor in 29% and good in 26% of cases. No clear statistical correlation was found between dental treatability and the number of diseases suffered by the subject. However, cardiovascular diseases and neurologic and mental disorders were found to reduce dental treatability more than other disorders.

On an optimal solution for maximizing the probability of retention in PPS sampling

A direct alternative proof of Keyfitz's optimal solution to the problem of maximizing the probability of retention in sampling on a second occasion is given, using techniques of elementary linear algebra. The proof and comments help one to better understand Keyfitz's solution, and they clearly demonstrate that the closed form solution of Keyfitz is one of a possible infinity of solutions offered by a linear programming approach. We also give one of those other solutions offered by linear programming, which is easy to obtain by hand calculations using only the operation of subtraction.

An alternative estimator for multiple characteristics in PPS sampling

Abstract The problem considered relates to large-scale sample surveys. A new estimator of population total for the characteristics that are poorly correlated with the selection probabilities has been developed for the PPSWR sampling scheme. The relative efficiency of the proposed estimator has been studied under a super-population model. A numerical investigation into the performance of the estimator has also been made.

πPS Sampling Scheme Through Grouping

AbstractA πPS sampling scheme is developed by combining Stevens and Midzuno‐Sen Sampling schemes. The restriction on original probabilities is less severe in the proposed scheme than that in Stevens and Midzuno‐Sen schemes. The performance of the scheme is satisfactory.

On Combination of Ratio and PPS Estimators

AbstractAGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample‐values. In this paper, an estimator depending on estimated optimum value of k based on sample‐values, under pps sampling scheme is proposed and studied.

Use of p‐auxiliary Variates in PPS Sampling

AbstractPresent study deals with the use of multivariate auxiliary information in selecting the samples in pps sampling.

Comparison of sampling strategies

Horvitz andThompson [1952] considered varying probability sampling method in general and furnished an unbiased estimator of the population total.Rao, Hartley andCochran [1962] proposed a simple procedure of unequal probability sampling with replacement. It leads to an estimator of the population total having smaller variance than is obtained by sampling with replacement. An attempt has been made in the present paper to compare efficiencies ofHorvitz-Thompson's estimator with that due toRao, hartley andCochran. It is demonstrated that the generalized πps sampling strategy consisting of the design with πi, the probability of inclusion of thei-th population unit in the sample proportional to the modified size together withHorvitz-Thompson's estimator is superior toRao, Hartley andCochran's sampling strategy under a general super-population model.

Horizontal Line Sampling in Upland Hardwoods

Abstract Continuous horizontal line sampling combines the advantages of PPS sampling and of strip cruising. Field work is concentrated on measuring trees. The method offers a choice of ways to control sample intensity. The direct estimate of a horizontal line sample is the sum of diameters per unit area of land. Tallying by diameter class permits calculation of tree frequency and number of trees per unit area of land. The average diameter calculated is the "average" assumed by nonforesters. Tally sheets may be formatted to show stocking percent, diameter growth required for full stocking, or volume.

An Application of Two-Stage Forest Sampling

Abstract A method of two-stage forest sampling is presented. The first stage is Bitterlich sampling, and the second stage (subsampling) is by PPS sampling. The method is suitable for use in updating an earlier survey or in returning to the field to obtain intensive measurement for the selected subsample trees after the first-stage sampling has been completed. The necessary equations are given and their use shown by numerical example.

πPS Sampling Schemes to Base HTE

πPS Sampling Schemes to Base HTE

Allocation to Strata and Relative Efficiencies of Stratified and Unstratified πPs Sampling Schemes

Summary The problem of optimum allocation to strata has been earlier examined in the light of a priori distributions. In this context, under the criterion of minimum expected variance, the sampling strategy consisting of an unstratified πPS sampling scheme together with the Horvitz–Thompson (HT) estimator was shown to be inferior to the strategy consisting of a stratified πPS sampling scheme with the corresponding HT estimator with this optimum allocation. In this paper, when stratification is based on the auxiliary information, we study whether a stratified πPS sampling strategy with various non-optimal allocations is likely to be worth while and whether it should be attempted at all. For populations commonly met in practice, we derive sufficient conditions for unstratified πPS sampling to be preferable to non-optimal stratified πPS sampling. An illustrative example is provided towards the end of the paper.

ON PPS SAMPLING WITHOUT REPLACEMENT ENSURING SELECTION PROBABILITIES EXACTLY PROPORTIONAL TO SIZES1

Australian Journal of StatisticsVolume 15, Issue 2 p. 87-94 ON PPS SAMPLING WITHOUT REPLACEMENT ENSURING SELECTION PROBABILITIES EXACTLY PROPORTIONAL TO SIZES1 M. N. Das, M. N. Das Institute of Agricultural Research Statistics, New Delhi-12, IndiaSearch for more papers by this authorS. Mohanty, S. Mohanty Institute of Agricultural Research Statistics, New Delhi-12, India *College of Agriculture, Orissa University of Agriculture and Technology, Bhubaneswar-3, India.Search for more papers by this author M. N. Das, M. N. Das Institute of Agricultural Research Statistics, New Delhi-12, IndiaSearch for more papers by this authorS. Mohanty, S. Mohanty Institute of Agricultural Research Statistics, New Delhi-12, India *College of Agriculture, Orissa University of Agriculture and Technology, Bhubaneswar-3, India.Search for more papers by this author First published: November 1973 https://doi.org/10.1111/j.1467-842X.1973.tb00012.xCitations: 2 ‡ Manuscript received October 18, 1971; revised March 30, 1972. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume15, Issue2November 1973Pages 87-94 RelatedInformation

HORVITZ‐THOMPSON AND DES RAJ ESTIMATORS REVISITED

SummaryIn this paper it is shown that the generalized πPS sampling strategy consisting of the design with πi, the probability of inclusion of the ith unit in the sample, proportional to the modified size together with the corresponding Horvitz‐Thompson estimator (Rao, 1971), is superior to the symmetrized Des Raj strategy under a general super‐population set‐up for all values of the super‐population parameter g, when the samples are of size two.

On the allocation of sample size in stratified sampling

The problem of optimum allocation of sample size to strata is examined in the light ofa priori distributions. In this context, we discuss with illustrations the justification for the assumption that the unknown proportionate values of σ 2 ’s can be replaced by the proportionate values of the known σ 2 ’s, which are estimates of σ 2 ’s. The sample size is allocated so as to minimize the expected variance of the strategy consisting of πPS sampling scheme and the Horvitz-Thompson estimator under a general super-population model. It is further shown that, in the sense of expected variance, πPS sampling for unstratified sampling is inferior to πPS stratified sampling with this type of allocation, unless the superpopulation parameterg attains the value 2, in which case both schemes are equivalent.

ON PPS SAMPLING WITH AND WITHOUT REPLACEMENT

ON PPS SAMPLING WITH AND WITHOUT REPLACEMENT

The Use of Systematic Sampling with Probability Proportionate to Size in a Large Scale Survey

Abstract Based on a nationwide labour force survey the gain in precision arising from systematic pps (probability proportionate to size) sampling of the primary sampling units as compared to with-replacement pps sampling is obtained. The performance of a particular convenient but biased estimator of sampling variance is also studied.

The Use of Systematic Sampling with Probability Proportionate to Size in a Large Scale Survey

Abstract Based on a nationwide labour force survey the gain in precision arising from systematic pps (probability proportionate to size) sampling of the primary sampling units as compared to with-replacement pps sampling is obtained. The performance of a particular convenient but biased estimator of sampling variance is also studied.