Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing

ABSTRACT

One of the important fields in statistics is testing hypothesis of
correlation coefficient. The extension of the idea of testing correlation to
fuzzy hypothesis is of great interesting. In this study, we examined the use of
fuzzy hypothesis testing approach for the Sequential Probability Ratio Test
(SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for
correlation coefficient with SPRT is illustrated by an example.

Cite this paper

S. Bacanli and D. Icen, "Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing,"*Open Journal of Statistics*, Vol. 3 No. 3, 2013, pp. 195-199. doi: 10.4236/ojs.2013.33022.

S. Bacanli and D. Icen, "Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing,"

References

[1] C. J. Kowalski, “The OC and ASN Functions of Some SPRT’s for the Correlation Coefficient,” Technometrics, Vol. 13, No. 4, 1971, pp. 833-840. doi:10.1080/00401706.1971.10488853

[2] A. Wald, “Sequential Analysis,” John Wiley & Sons, Inc., New York, 1947.

[3] S. C. Choi, “Sequential Test for Correlation Coefficients,” Journal of the American Statistical Association, Vol. 66, No. 335, 1971, pp. 575-576. doi:10.1080/01621459.1971.10482308

[4] M. Pradhan and Y. S. Sathe, “An Unbiased Estimator and a Sequential Test for the Correlation Coefficient,” Journal of the American Statistical Association, Vol. 70, No. 349, 1975, pp. 160-161. doi:10.1080/01621459.1975.10480278

[5] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X

[6] S. M. Taheri and J. Behboodian, “Neyman-Pearson Lemma for Fuzzy Hypotheses Testing,” Metrika, Vol. 64, No. 3, 2006, pp. 289-304. doi:10.1007/s00184-006-0049-8

[7] H. Torabi and J. Behboodian, “Sequential Probability Ratio Test for Fuzzy Hypotheses Testing with Vague Data,” Austrian Journal of Statistics, Vol. 34, No. 1, 2005, pp. 25-38.

[8] R. Talukdar and H. K. Baruah, “Sequential Probability Ratio Test with Fuzzy Observations,” The Journal of Fuzzy Mathematics, Vol. 15, No. 3, 2007, pp. 627-643.

[9] H. Torabi and S. M. Mirhosseini, “Sequential Probability Ratio Tests for Fuzzy Hypotheses Testing,” Applied Mathematical Sciences, Vol. 3, No. 33, 2009, pp. 1609-1618.

[10] M. G. Akbari, “Sequential Test of Fuzzy Hypothesis,” American Journal of Statistics, Vol. 1, No. 2, 2011, pp. 87-92. doi:10.4236/ojs.2011.12010

[11] C. H. Leu, C. C. Chen, and C. M. Lai, “Testing Hypothesis Concerning Correlation Coefficient with Fuzzy Data,” 5th International Conference on Fuzzy Systems and Know ledge Discovery, Jinan, 18-20 October 2008, pp. 635-643. doi:10.1109/FSKD.2008.352

[12] H. Torabi and J. Behboodian, “Likelihood Ratio Tests for Fuzzy Hypothesis Testing,” Statistical Papers, Vol. 48, No. 3, 2007, pp. 509-522. doi:10.1007/s00362-006-0352-5

[1] C. J. Kowalski, “The OC and ASN Functions of Some SPRT’s for the Correlation Coefficient,” Technometrics, Vol. 13, No. 4, 1971, pp. 833-840. doi:10.1080/00401706.1971.10488853

[2] A. Wald, “Sequential Analysis,” John Wiley & Sons, Inc., New York, 1947.

[3] S. C. Choi, “Sequential Test for Correlation Coefficients,” Journal of the American Statistical Association, Vol. 66, No. 335, 1971, pp. 575-576. doi:10.1080/01621459.1971.10482308

[4] M. Pradhan and Y. S. Sathe, “An Unbiased Estimator and a Sequential Test for the Correlation Coefficient,” Journal of the American Statistical Association, Vol. 70, No. 349, 1975, pp. 160-161. doi:10.1080/01621459.1975.10480278

[5] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X

[6] S. M. Taheri and J. Behboodian, “Neyman-Pearson Lemma for Fuzzy Hypotheses Testing,” Metrika, Vol. 64, No. 3, 2006, pp. 289-304. doi:10.1007/s00184-006-0049-8

[7] H. Torabi and J. Behboodian, “Sequential Probability Ratio Test for Fuzzy Hypotheses Testing with Vague Data,” Austrian Journal of Statistics, Vol. 34, No. 1, 2005, pp. 25-38.

[8] R. Talukdar and H. K. Baruah, “Sequential Probability Ratio Test with Fuzzy Observations,” The Journal of Fuzzy Mathematics, Vol. 15, No. 3, 2007, pp. 627-643.

[9] H. Torabi and S. M. Mirhosseini, “Sequential Probability Ratio Tests for Fuzzy Hypotheses Testing,” Applied Mathematical Sciences, Vol. 3, No. 33, 2009, pp. 1609-1618.

[10] M. G. Akbari, “Sequential Test of Fuzzy Hypothesis,” American Journal of Statistics, Vol. 1, No. 2, 2011, pp. 87-92. doi:10.4236/ojs.2011.12010

[11] C. H. Leu, C. C. Chen, and C. M. Lai, “Testing Hypothesis Concerning Correlation Coefficient with Fuzzy Data,” 5th International Conference on Fuzzy Systems and Know ledge Discovery, Jinan, 18-20 October 2008, pp. 635-643. doi:10.1109/FSKD.2008.352

[12] H. Torabi and J. Behboodian, “Likelihood Ratio Tests for Fuzzy Hypothesis Testing,” Statistical Papers, Vol. 48, No. 3, 2007, pp. 509-522. doi:10.1007/s00362-006-0352-5