Statistical inference with randomized nomination sampling

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Date
2014-05, 2014-08
Authors
Nourmohammadi, Mohammad
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Publisher
Elsevier B.V.
Indian Statistical Institute
Abstract
In this dissertation, we develop several new inference procedures that are based on randomized nomination sampling (RNS). The first problem we consider is that of constructing distribution-free confidence intervals for quantiles for finite populations. The required algorithms for computing coverage probabilities of the proposed confidence intervals are presented. The second problem we address is that of constructing nonparametric confidence intervals for infinite populations. We describe the procedures for constructing confidence intervals and compare the constructed confidence intervals in the RNS setting, both in perfect and imperfect ranking scenario, with their simple random sampling (SRS) counterparts. Recommendations for choosing the design parameters are made to achieve shorter confidence intervals than their SRS counterparts. The third problem we investigate is the construction of tolerance intervals using the RNS technique. We describe the procedures of constructing one- and two-sided RNS tolerance intervals and investigate the sample sizes required to achieve tolerance intervals which contain the determined proportions of the underlying population. We also investigate the efficiency of RNS-based tolerance intervals compared with their corresponding intervals based on SRS. A new method for estimating ranking error probabilities is proposed. The final problem we consider is that of parametric inference based on RNS. We introduce different data types associated with different situation that one might encounter using the RNS design and provide the maximum likelihood (ML) and the method of moments (MM) estimators of the parameters in two classes of distributions; proportional hazard rate (PHR) and proportional reverse hazard rate (PRHR) models.
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Keywords
Randomized nomination sampling, Confidence interval, Tolerance interval, Finite population, Infinite population, Proportional hazard rate model, Maximum likelihood, Method of moment
Citation
Nourmohammadi, M., Jafari Jozani, M., & Johnson, B. C. (2014). Confidence intervals for quantiles in finite populations with randomized nomination sampling. Computational Statistics & Data Analysis, 73, 112-128.
Nourmohammadi, M., Jozani, M. J., & Johnson, B. C. Nonparametric Confidence Intervals for Quantiles with Randomized Nomination Sampling. Sankhya A, 1-25.