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Choice of the spectral window width by cross-validation: case of the almost periodically correlated process with continuous time. (English. French summary) Zbl 1504.62139

Summary: This work presents a procedure to choose the width of the spectral window used in the smoothing of a periodogram when estimating the spectral density of an almost periodically correlated process. The cross-validation procedure we propose is based on the estimation of the integrated square error by using the “Leave-out-I” principle.

MSC:

62M15 Inference from stochastic processes and spectral analysis
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
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References:

[1] Arlot. S and Lerasle. M. (2001). Choice of V for V-Fold cross-validation in Least-Square Density Estimation. Journal of Machine Learning Research. 17. 1-50. · Zbl 1434.62041
[2] Bowman A .W, (1984). an alternative method of cross-validation for smoothing of density estimates. Biometrika, 71(2), 253-360.
[3] Ekra. S. P and Monsan. V, (2021). Asymptotic property of spectral density estimators of a continuous time process almost periodically correlated low dependent by poisson, Far East Journal of Theoretical Statistics 61(2), 145-189. Doi.org/10.17654/TS061020145. · Zbl 1499.62123
[4] Gregoire G, (1993). Least squares cross-validation for counting process intensities, Scand. J. Statis. 20, 343-360. · Zbl 0795.62031
[5] Hurd. H. L and Leskow. J, (1992). Estimation of the Fourier coefficient functions and their spectral densities for mixing almost periodically correlated processes. Statist. Probab. Lett. 14(1992), 299-306. · Zbl 0752.62067
[6] Khadijetou. E. H (2019). Choix optimal du paramètre de lissage dans l’estimation no paramétrique de la fonction de densité pour des processus stationnaires à temps continu. Université du Littoral côte d’Opale. École doctorale EDSPI Lille
[7] Krueger.T, Panknin. D and Braun. M. (2015). Fast cross-validation via sequential testing. Journal of Machine Learning Research, 16: 1103-1155. · Zbl 1351.62099
[8] Marron J.S and Härdle W (1986). Random approximations to some measures of accuracy in nonparametric curve estimation. J. Multivariate Anal. 20.91-113. · Zbl 0608.62045
[9] Messaci F (1986). Estimation de la densité spectrale d’un processus en temps continu par échantillonnage poissonnien. Thése de 3éme cycle à l’université Rouen.
[10] Monsan V, Dehay D (2007). Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes. Stat Infer Stoch Process 10:223-253 DOI 10.1007/s11203-006-0004-3. · Zbl 1144.62078
[11] Rachdi M. (1998). Choix de la largeur de fenêtre spectrale par validation croisée. Analyse spectrale p-adique. Thèse de doctorat à l’université de Rouen. · Zbl 0912.62102
[12] Rachdi M (1998). Choix de la largeur de fenêtre spectral par validation croisée pour un processus stationnaire à temps continue. C.R. Acad. Sci, Paris, t. 327, série I, 777-780. · Zbl 0912.62102
[13] Rudemo M (1982). Emperical choice of histograms and kernel density estimators. Scand.j. Stat., 9, 65-78. · Zbl 0501.62028
[14] Sabre. R (1994). Estimation de la densité de la mesure spectrale mixte pour un processus symétrique stable strictement stationaire. C. R. Acad. Sci., Paris, t. 319, Série I, p . 1307-1310. · Zbl 0814.60031
[15] Sabre. R (1995). Spectral density estimation for stationary stable random fields. Journal Applicationes Mathematicae, 23, 2, p, 107-133 · Zbl 0846.62067
[16] Salima. T. H, Youndje. Elie. (2003). Validation croisée pour l’estimateur lissé de la fonction de hasard : cas des données censurées. Revue de statistique appliquée, tone 51, (1).p.73-86.
[17] Sarda P and Vieu P (1989). Estimation non paramétrique de la fonction de hasard. Neuvième rencontre franco-belge de Statisticiens, cahier du CERO, 31, (3-4), 241-265. · Zbl 0683.62021
[18] Stone, C. J.(1984). An asymptotically optimal window selection rule for kernel density estimates. Annals of Statistics 12: 1285-1297. · Zbl 0599.62052
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