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Testing for No Effect by Cosine Series Methods

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  • R. L. Eubank

Abstract

The properties of three lack‐of‐fit tests that are related to non‐parametric cosine regression analysis are examined in the context of testing for a constant mean function. Analytic power comparisons of these tests vs a most powerful test are made using intermediate asymptotic relative efficiency. In particular, a data‐driven test is produced which is asymptotically as efficient as the most powerful test over a class of alternatives. A small scale simulation experiment is conducted to ascertain the extent that the large sample comparisons are applicable to finite samples.

Suggested Citation

  • R. L. Eubank, 2000. "Testing for No Effect by Cosine Series Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 747-763, December.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:4:p:747-763
    DOI: 10.1111/1467-9469.00220
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    Cited by:

    1. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    2. Teresa Ledwina & Grzegorz Wyłupek, 2012. "Nonparametric tests for stochastic ordering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 730-756, December.
    3. Chin-Shang Li, 2012. "Testing for no effect via splines," Computational Statistics, Springer, vol. 27(2), pages 343-357, June.
    4. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.
    5. Choi, Taeryon & Lee, Jaeyong & Roy, Anindya, 2009. "A note on the Bayes factor in a semiparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1316-1327, July.
    6. Mason David M. & Eubank Randy, 2012. "Moderate deviations and intermediate efficiency for lack-of-fit tests," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 175-187, June.
    7. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    8. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 62-82, March.

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