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Year 2019, Volume: 68 Issue: 1, 98 - 110, 01.02.2019

Halil Tanıl

https://doi.org/10.31801/cfsuasmas.443648

Abstract

References

  • Ahsanullah, M. (2004). Record Values-Theory and Applications. Universiy Press of America, Lanham, MD.
  • Aiyer, R. J., Guilliter, C. L. and Albers, W. (1979). Asymptotic relative efficiencies of rank tests for trend alternatives. Journal of American Statistical Association. 74, 226-231.
  • Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998). Records. John Wiley, New York.
  • Chandler, K.N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B. 14, 220-228.
  • Cox, D.R. and Stuart, A. (1955). Some quick sign tests for trend in location and dispersion. Biometrika 42, 80-95.
  • Daniels, H.E., (1950). Rank correlation and population models. Journal of Royal Statistical Society Series B. 12, 171-181.
  • Diersen, J. and Trenkler, G. (1996). Records Tests for Trend in Location. Statistics. 28, 1-12.
  • Dziubdziela, W. and Kopocinski, B. (1976). Limiting properties of the k-th record values. Appl. Math. 15, 187-190.
  • Foster, F.G. and Stuart, A. (1954). Distribution-free tests in time-series based on the breaking of records (with discussions). Journal of the Royal Statistical Society, Series B. 16, 2-22.
  • Hofmann, G. and Balakrishnan, N. (2006). A nonparametric test for trend based on initial ranks. Journal of Statistical Computation and Simulation. 76, 829-837.
  • Kamps, U. (1995). A Concept of Generalized Order Statistics. Stuttgart: Teubner.
  • Khraibani, Z., Jacob, C., Ducrot, C., Charras-Garrido, M. and Sala C. (2015). A non parametric exact test based on the number of records for an early detection of emerging events: Illustration in epidemiology. Communications in Statistics-Theory and Methods. 44, 726-749.
  • Kozan, A. and Tanil, H. (2013). Bottom-k-Lists. İstatistik: Journal of the Turkish Statistical Association. 6, 73-79.
  • López-Blázquez, F. and Wesołowski, J. (2007). Top-k-lists. Metrika. 65, 69--82.
  • Mann, H. B. (1945). Nonparametric test against trend. Econometrica. 13, 245-259.
  • Moore, G. H. and Wallis, W. A. (1943). Time series significance tests based on signs of differences. J. Amer. Statist. Ass. 38, 153-164.
  • Nevzorov, V. (1988). Records. Theor. Prob. Appl. 32, 201-228.
  • Nevzorov, V. (2000). Records: Mathematical Theory. Translation Mathematical Monographs Volume 194, American Mathematical Society, Province, RI 02940, USA.
  • Razmkhah, M. and Ahmadi, J. (2013). Pitman closeness of current k-records to population quantiles. Statistics & Probability Letters. 83, 148-156.
  • Redner, S. and Petersen, M. R. (2006). Role of global warming on the statistics of record-breaking temperatures. Physical Review E 74, 061114.
  • Stuart, A. (1954). Asymptotic relative efficiencies of distribution-free tests of randomness against normal alternatives. Journal of American Statistical Association. 49, 147-157.
  • Stuart, A. (1956). The efficiencies of tests of randomness against normal regression. Journal of American Statistical Association. 51, 285-287.
  • Wald, A. and Wolfowitz, J. (1943). An exact test for randomness in the non-parametric case based on serial correlation. Ann. Math. Statist. 14, 378-388.
  • Wallis, W. A. and Moore, G. H. (1941). A significance test for time series analysis. J. Amer. Statist. Ass. 36, 401-409.

A Generalized Version of Foster and Stuart's d-statistic

Year 2019, Volume: 68 Issue: 1, 98 - 110, 01.02.2019

Halil Tanıl

https://doi.org/10.31801/cfsuasmas.443648

Abstract

Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in. In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation. The exact and asymptotic distributions of the proposed test statistic are obtained for a random continuous sequence which is independent and identically distributed (i.i.d.). Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.

Keywords

Monotonic trend in location kth-records Top-k-lists; Bottom-k-lists Distribution-free test Empirical power comparison

References

  • Ahsanullah, M. (2004). Record Values-Theory and Applications. Universiy Press of America, Lanham, MD.
  • Aiyer, R. J., Guilliter, C. L. and Albers, W. (1979). Asymptotic relative efficiencies of rank tests for trend alternatives. Journal of American Statistical Association. 74, 226-231.
  • Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998). Records. John Wiley, New York.
  • Chandler, K.N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B. 14, 220-228.
  • Cox, D.R. and Stuart, A. (1955). Some quick sign tests for trend in location and dispersion. Biometrika 42, 80-95.
  • Daniels, H.E., (1950). Rank correlation and population models. Journal of Royal Statistical Society Series B. 12, 171-181.
  • Diersen, J. and Trenkler, G. (1996). Records Tests for Trend in Location. Statistics. 28, 1-12.
  • Dziubdziela, W. and Kopocinski, B. (1976). Limiting properties of the k-th record values. Appl. Math. 15, 187-190.
  • Foster, F.G. and Stuart, A. (1954). Distribution-free tests in time-series based on the breaking of records (with discussions). Journal of the Royal Statistical Society, Series B. 16, 2-22.
  • Hofmann, G. and Balakrishnan, N. (2006). A nonparametric test for trend based on initial ranks. Journal of Statistical Computation and Simulation. 76, 829-837.
  • Kamps, U. (1995). A Concept of Generalized Order Statistics. Stuttgart: Teubner.
  • Khraibani, Z., Jacob, C., Ducrot, C., Charras-Garrido, M. and Sala C. (2015). A non parametric exact test based on the number of records for an early detection of emerging events: Illustration in epidemiology. Communications in Statistics-Theory and Methods. 44, 726-749.
  • Kozan, A. and Tanil, H. (2013). Bottom-k-Lists. İstatistik: Journal of the Turkish Statistical Association. 6, 73-79.
  • López-Blázquez, F. and Wesołowski, J. (2007). Top-k-lists. Metrika. 65, 69--82.
  • Mann, H. B. (1945). Nonparametric test against trend. Econometrica. 13, 245-259.
  • Moore, G. H. and Wallis, W. A. (1943). Time series significance tests based on signs of differences. J. Amer. Statist. Ass. 38, 153-164.
  • Nevzorov, V. (1988). Records. Theor. Prob. Appl. 32, 201-228.
  • Nevzorov, V. (2000). Records: Mathematical Theory. Translation Mathematical Monographs Volume 194, American Mathematical Society, Province, RI 02940, USA.
  • Razmkhah, M. and Ahmadi, J. (2013). Pitman closeness of current k-records to population quantiles. Statistics & Probability Letters. 83, 148-156.
  • Redner, S. and Petersen, M. R. (2006). Role of global warming on the statistics of record-breaking temperatures. Physical Review E 74, 061114.
  • Stuart, A. (1954). Asymptotic relative efficiencies of distribution-free tests of randomness against normal alternatives. Journal of American Statistical Association. 49, 147-157.
  • Stuart, A. (1956). The efficiencies of tests of randomness against normal regression. Journal of American Statistical Association. 51, 285-287.
  • Wald, A. and Wolfowitz, J. (1943). An exact test for randomness in the non-parametric case based on serial correlation. Ann. Math. Statist. 14, 378-388.
  • Wallis, W. A. and Moore, G. H. (1941). A significance test for time series analysis. J. Amer. Statist. Ass. 36, 401-409.
There are 24 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Halil Tanıl 0000-0001-5402-8859

Publication Date February 1, 2019
Submission Date March 28, 2017
Acceptance Date October 25, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Tanıl, H. (2019). A Generalized Version of Foster and Stuart’s d-statistic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 98-110. https://doi.org/10.31801/cfsuasmas.443648
AMA Tanıl H. A Generalized Version of Foster and Stuart’s d-statistic. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):98-110. doi:10.31801/cfsuasmas.443648
Chicago Tanıl, Halil. “A Generalized Version of Foster and Stuart’s D-Statistic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 98-110. https://doi.org/10.31801/cfsuasmas.443648.
EndNote Tanıl H (February 1, 2019) A Generalized Version of Foster and Stuart’s d-statistic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 98–110.
IEEE H. Tanıl, “A Generalized Version of Foster and Stuart’s d-statistic”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 98–110, 2019, doi: 10.31801/cfsuasmas.443648.
ISNAD Tanıl, Halil. “A Generalized Version of Foster and Stuart’s D-Statistic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 98-110. https://doi.org/10.31801/cfsuasmas.443648.
JAMA Tanıl H. A Generalized Version of Foster and Stuart’s d-statistic. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:98–110.
MLA Tanıl, Halil. “A Generalized Version of Foster and Stuart’s D-Statistic”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 98-110, doi:10.31801/cfsuasmas.443648.
Vancouver Tanıl H. A Generalized Version of Foster and Stuart’s d-statistic. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):98-110.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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