Title:
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A class of tests for exponentiality based on a continuum of moment conditions (English) |
Author:
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Meintanis, Simos G. |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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45 |
Issue:
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6 |
Year:
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2009 |
Pages:
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946-959 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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The empirical moment process is utilized to construct a family of tests for the null hypothesis that a random variable is exponentially distributed. The tests are consistent against the 'new better than used in expectation' (NBUE) class of alternatives. Consistency is shown and the limit null distribution of the test statistic is derived, while efficiency results are also provided. The finite-sample properties of the proposed procedure in comparison to more standard procedures are investigated via simulation. (English) |
Keyword:
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goodness-of-fit test |
Keyword:
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empirical moments |
Keyword:
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ageing distributions |
Keyword:
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Bahadur efficiency |
MSC:
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62E20 |
MSC:
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62G10 |
MSC:
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62G20 |
MSC:
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62N05 |
MSC:
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65C60 |
idZBL:
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Zbl pZbl 1186.62056 |
idMR:
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MR2650075 |
. |
Date available:
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2010-06-02T19:26:30Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140031 |
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Reference:
|
[1] I. A. Ahmad: Moment inequalities of aging families of distributions with hypothesis testing applications.J. Statist. Plann. Infer. 92 (2001), 121–132. MR 1809700 |
Reference:
|
[2] R. R. Bahadur: Stochastic comparison of tests.Ann. Math. Statist. 31 (1960), 276–295. Zbl 0201.52203, MR 0116413 |
Reference:
|
[3] V. Bening and V. Korolev: Estimation problems for fractional stable distributions.In: Trans. XXIV Internat. Seminar on Stability Problems for Stochastic Models 2004 (Andronov et al., eds.), Transport and Telecommunication Institute, Riga, Latvia, pp. 270–276. |
Reference:
|
[4] M. Carrasco and J.-P. Florens: Generalization of GMM to a continuum of moment conditions.Econometr. Theory 16 (2000), 797–834. MR 1803711 |
Reference:
|
[5] M. Carrasco and J.-P. Florens: Simulation-based method of moments and efficiency.J. Bus. Econom. Statist. 20 (2002), 482–492. MR 1945605 |
Reference:
|
[6] G. Chaudhuri: Testing exponentiality against $L$-distributions.J. Statist. Plann. Infer. 64 (1997), 249–255. Zbl 0914.62030, MR 1621616 |
Reference:
|
[7] H. Cramér: Mathematical Methods of Statistics.Princeton University Press, Princeton 1946. MR 0016588 |
Reference:
|
[8] R. D’Agostino and M. Stephens: Goodness-of-Fit Techniques.Marcel Dekker, New York 1986. MR 0874534 |
Reference:
|
[9] B. S. Dhillon: Lifetime distributions.IEEE Trans. Reliability 30 (1981), 457–459. |
Reference:
|
[10] K. A. Doksum and B. S. Yandell: Tests for exponentiality.In: Handbook of Statistics 4: Nonparametric methods (Krishnaiah and Sen, eds.), North-Holland, Amsterdam 1984, pp. 579–611. MR 0831730 |
Reference:
|
[11] T. W. Epps and L. B. Pulley: A test for exponentiality vs.monotone hazard alternatives derived from the empirical characteristic function. J. Roy. Statist. Soc. B48 (1986), 206–213. MR 0867998 |
Reference:
|
[12] N. Henze and B. Klar: Testing exponentiality against the ${\cal {L}}$-class of life distributions.Math. Method. Statist. 10 (2001), 232–246. MR 1852070 |
Reference:
|
[13] N. Henze and S. G. Meintanis: Recent and classical tests for exponentiality: a partial review with comparisons.Metrika 61 (2005), 29–45. MR 2126435 |
Reference:
|
[14] B. Klar: A class of tests for exponentiality against HNBUE alternatives.Statist. Probab. Lett. 47 (2000), 199–207. Zbl 0977.62103, MR 1747107 |
Reference:
|
[15] S. G. Meintanis: Efficient moment-type estimation in exponentiated laws.Math. Methods Statist. 15 (2007), 444–455. MR 2301661 |
Reference:
|
[16] M. Mitra and S. K. Basu: On a nonparametric family of life distributions and its dual.J. Statist. Plann. Infer. 39 (1994), 385–397. MR 1278590 |
Reference:
|
[17] A. R. Mugdadi and I. A. Ahmad: Moment inequalities derived from comparing life with its equilibrium form.J. Statist. Plann. Infer. 134 (2005), 303–317. MR 2200060 |
Reference:
|
[18] Ya. Yu. Nikitin: Asymptotic Efficiency of Nonparametric Tests.Cambridge University Press, New York 1995. Zbl 1171.62031, MR 1415127 |
Reference:
|
[19] B. L. S. Prakasa Rao: Asymptotic Theory of Statistical Inference.Wiley, New York 1987. Zbl 0604.62025, MR 0874342 |
Reference:
|
[20] F. Rublík: On optimality of the LR tests in the sence of exact slopes.I. General case. Kybernetika 25 (1989), 13–25. MR 0987853 |
Reference:
|
[21] F. Rublík: On optimality of the LR tests in the sence of exact slopes.II. Application to individual distributions. Kybernetika 25 (1989), 117–135. MR 0995954 |
Reference:
|
[22] A. I. Zayed: Handbook of Function and Generalized Function Transformations.CRC Press, New York 1996. Zbl 0851.44002, MR 1392476 |
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