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Some variants of adaptive sampling procedures and their applications

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  • Sengupta, Raghu Nandan
  • Sengupta, Angana
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    Abstract

    Sequential analysis as a sampling technique facilitates efficient statistical inference by considering less number of observations in comparison to the fixed sampling method. The optimal stopping rule dictates the sample size and also the statistical inference deduced thereafter. In this research we propose three variants of the already existing multistage sampling procedures and name them as (i) Jump and Crawl (JC), (ii) Batch Crawl and Jump (BCJ) and (iii) Batch Jump and Crawl (BJC) sequential sampling methods. We use the (i) normal, (ii) exponential, (iii) gamma and (iv) extreme value distributions for the point estimation problems under bounded risk conditions. We highlight the efficacy of using the right adaptive sampling plan for the bounded risk problems for these four distributions, considering two different loss functions, namely (i) squared error loss (SEL) and (ii) linear exponential (LINEX) loss functions. Comparison and analysis of our proposed methods with existing sequential sampling techniques is undertaken and the importance of this study is highlighted using extensive theoretical simulation runs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 12 (December)
    Pages: 3183-3196

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3183-3196

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Decision analysis Normal Exponential Gamma Extreme value Sequential sampling Loss functions Squared error loss Linear exponential loss Bounded risk Simulation Business applications;

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    1. Cui, Yin & Fu, Yuejiao & Hussein, Abdulkadir, 2009. "Group sequential testing of homogeneity in genetic linkage analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3630-3639, August.
    2. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    3. Raghu Nandan Sengupta, 2008. "Use of asymmetric loss functions in sequential estimation problems for multiple linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 245-261.
    4. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
    5. Alp, Tansel & Demetrescu, Matei, 2010. "Joint forecasts of Dow Jones stocks under general multivariate loss function," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2360-2371, November.
    6. Salvan, Alessandra, 1990. "Planning sequential clinical trials: A review," Computational Statistics & Data Analysis, Elsevier, vol. 9(1), pages 47-56, January.
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