Ranked Set Sampling Approach for Estimating Response of Developmental Programs with Linear Impacts under Successive Phases.

Girish Chandra; Rajiv Pandey; DS Bhoj; Raman Nautiyal; Jawaid Ashraf; MedRam Verma

Author(s)

Girish Chandra Division of Forest Statistics, Indian Council of Forestry Research and Education, Dehradun-248006, India

Rajiv Pandey Indian Council of Forestry Research and Education, Dehradun-248006, India

DS Bhoj Department of Mathematical Sciences, Rutgers University, Camden, USA

Raman Nautiyal Division of Forest Statistics, Indian Council of Forestry Research and Education, Dehradun-248006, India

Jawaid Ashraf Indian Council of Forestry Research and Education, Dehradun-248006, India

MedRam Verma ICAR-Indian Veterinary Research Institute, Bareilly, India

Abstract

The problem of estimation is motivated by some studies from the area of developmental programs management to be implemented by the government and non-government organizations under different phases. The examples of such programs are educational programs, women empowerment programs for enhancing gross enrollment ratio in a region. There are two important variables in such programs. One of the variables is called the survey variable. The survey variable changes under the impact of the program over different phases and is termed as the response variable. In our study, we consider linear impacts of the programs under successive phases and multiplicative model which relates the response and survey variables. The management of the programs is interested in estimation of the mean of the response variable. Therefore, in this paper, we propose an unbiased estimator of the population mean of the response variable by using ranked set sampling procedure on the survey variable. The estimator is then compared with the estimator based on simple random sample (SRS). The relative precisions of the proposed estimator with the estimator based on SRS are computed for some symmetric and skew distributions. It is shown that the gains in relative precisions of the proposed estimator are substantial for all sample sizes and the chosen distributions. We applied the formulas derived in this paper to one real life example from India?s report, Education for all towards quality with equity, of National University of Education Planning and Administration, New Delhi, 2014.

Publication Details

Page(s) 163-176

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 34, Issue: 2, Year: 2018

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Keywords

Order Statistics, symmetric distribution., skewed distribution, relative precision

References

Aragon , M.E.D.,Patil , G.P.,Taillie , C., 1999.A performance indicator for ranked set sampling using ranking error probability matrix,Environmental and Ecological Statistics 6 75 -89

Bhoj , D.S., 2001.Ranked set sampling with unequal samples,Biometrics 57 957 -962

Bohn , L.L.,Wolfe , D.A., 1994.The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann-WhiteyWilcoxon statistic,Journal of the American Statistical Association 89 168 -176

Chandra , G.,Tiwari , N.,Chandra , H., 2011.Adaptive cluster sampling based on ranked sets,Metodoloski Zvezki 8 39 -55

Chen , H.,Stasny , E.A.,Wolfe , D.A., 2006.An empirical assessment of ranking accuracy in ranked set sampling,Computational Statistics and Data Analysis 51 1411 -1419

Chen , Z.,Bai , Z.D.,Sinha , B.K., 2004.Ranked set sampling: theory and applications, -

Chen , Z.,Stasny , E.A.,Wolfe , D.A., 2003.Improved estimation of disease prevalence using ranked set sampling,Technical Report Number 718 -

Chen , Z.,Stasny , E.A.,Wolfe , D.A., 2005.Ranked set sampling for efficient estimation of a population proportion, 24 3319 -29

Cochran , W.G., 1977.Sampling techniques, -

Dell , T.R.,Clutter , J.L., 1972.Ranked set sampling theory with order statistics background,Biometrics 28 545 -555

Fligner , M.A.,MacEachern , S.N., 2006.Nonparametric two-sample methods for ranked-set sample data,Journal of the American Statistical Association 101 1107 -1118

Harter , H.L.,Balakrishnan , N, 1996.CRC handbook of tables for the use of order statistics in estimation, -

Hettmansperger , T.P., 1995.The ranked-set sampling sign test,Nonparametric Statistics 4 263 -270

Husby , C.E.,Stansy , E.A.,Wolfe , D.A., 2005.An application of ranked set sampling for mean and median estimation using USDA crop production data,Journal of Agricultural 10 354 -373

Johnson , G.D., Paul, G.P.,Sinha , A.K., 1993.Ranked set sampling for vegetation research,Abstracta Botanica 17 87 -102

Kaur , A.,Patil , G.P.,Taillie , C., 1997.Unequal allocation models for ranked set sampling with skew distributions,Biometrics 53 123 -130

Khan , L.,Shabbir , J., 2016.Improved ratio-type estimators of population mean in ranked set sampling using two concomitant variables,Pakistan Journal of Statistics and Operational Research 12 507 -518

Khan , L.,Shabbir , J.,Kadilar , C., 2016.Efficient classes of ratio-type estimators of population mean under stratified median ranked set sampling,Pakistan Journal of Statistics 32 475 -496

Kowalczyk , B., 2005.Alternative sampling designs some applications of qualitative data in survey sampling, 7 427 -443

McIntyre , G.A., 1952.A method for unbiased selective sampling using ranked sets,Australian Journal of Agricultural Research 3 385 -390

McIntyre , G.A., 1978.Commonwealth Bureau of Pastures and Field Crops,Measurement of Grassland Vegetation and Animal Production Bulletin 8 21 -

Nahhas , R.W.,Wolfe , D.A.,Chen , H., 2002.Ranked set sampling: cost and optimal set size,Biometrics 58 964 -971

Pandey , R.,SeriesA, 2010.Samples allocation decisions for program evaluation: a case of multiplicative effect on units due to developmental initiatives in phased manner,Folia Forestalia Polonica 52 83 -88

Pandey , R.,Verma , M.R., 2008.Samples allocation in different strata for impact evaluation of developmental programme,Rev. Mat. Estat 26 103 -112

Pandey , R.,Ashraf , J.,Verma , M.R., 2012.Proportional allocation stratum weight for population units under external impact attributed to binomial functions in successive strata,International Journal of Mathematics Sciences and Applications 2 867 -872

Takahasi , K.,Wakimoto , K., 1968.On unbiased estimates of the population mean based on the sample stratified by means of ordering,Annals of the Institute of Statistical Mathematics 20 1 -31

Tiwari , N.,Chandra , G., 2011.A systematic approach for unequal allocations in ranked set sampling with skew distributions,Journal of the Indian Society of Agricultural Statistics 65 331 -338

Verma , M.R.,Singh , B.,Pandey , R.,Joorel , J.P.S., 2014.Sample allocation procedure for evaluation of the impact of development programme under exponential phase effect,Journal of the Indian Statistical Association 52 151 -160

Zamanzade , E.,Mahdizadeh , M., 2016.Entropy estimation from judgment post stratified data,Pakistan Journal of Statistics and Operation Research 4 625 -637