@article{aa95390944ff47b7b59b065957bc9b0d,
title = "Statistical inference for quantiles in the frequency domain",
abstract = "For second-order stationary processes, the spectral distribution function is uniquely determined by the autocovariance function of the process. We define the quantiles of the spectral distribution function in frequency domain. The estimation of quantiles for second-order stationary processes is considered by minimizing the so-called check function. The quantile estimator is shown to be asymptotically normal. We also consider a hypothesis testing for quantiles in frequency domain and propose a test statistic associated with our quantile estimator, which asymptotically converges to standard normal under the null hypothesis. The finite sample performance of the quantile estimator is shown in our numerical studies.",
keywords = "Asymptotic distribution, Frequency domain, Periodogram, Quantile test, Stationary process",
author = "Yan Liu",
note = "Funding Information: Acknowledgements The author would like to sincerely thank editors Professor Marc Hallin and Professor Yury A. Kutoyants, and two referees for their comments on the original manuscript. Especially, the discussion on the proof with two referees and R-code shared by a referee led to a great improvement of the manuscript. He also would like to thank the guest editor Professor Masanobu Taniguchi for his suggestions and encouragements. This work was supported by Grant-in-Aid for Young Scientists (B) (17K12652). Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media B.V.",
year = "2017",
month = oct,
day = "1",
doi = "10.1007/s11203-017-9166-4",
language = "English",
volume = "20",
pages = "369--386",
journal = "Statistical Inference for Stochastic Processes",
issn = "1387-0874",
publisher = "Springer Netherlands",
number = "3",
}