@article{TVP_2013_58_3_a6,
author = {M. Ruiz-Medina and R. Crujeiras},
title = {A central limit result in the wavelet domain for minimum contrast estimation of fractal random fields},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {550--583},
year = {2013},
volume = {58},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_3_a6/}
}
TY - JOUR AU - M. Ruiz-Medina AU - R. Crujeiras TI - A central limit result in the wavelet domain for minimum contrast estimation of fractal random fields JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2013 SP - 550 EP - 583 VL - 58 IS - 3 UR - http://geodesic.mathdoc.fr/item/TVP_2013_58_3_a6/ LA - en ID - TVP_2013_58_3_a6 ER -
%0 Journal Article %A M. Ruiz-Medina %A R. Crujeiras %T A central limit result in the wavelet domain for minimum contrast estimation of fractal random fields %J Teoriâ veroâtnostej i ee primeneniâ %D 2013 %P 550-583 %V 58 %N 3 %U http://geodesic.mathdoc.fr/item/TVP_2013_58_3_a6/ %G en %F TVP_2013_58_3_a6
M. Ruiz-Medina; R. Crujeiras. A central limit result in the wavelet domain for minimum contrast estimation of fractal random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 3, pp. 550-583. http://geodesic.mathdoc.fr/item/TVP_2013_58_3_a6/
[1] Adler R. J., The Geometry of Random Fields, John Wiley, New York, 1981, 280 pp. | MR | Zbl
[2] Abry P., Transformées en ondelettes Analyses multirésolutions et signaux de pression en turbulance, Doct. diss., Univ. Claude Bernard, France, Lyon, 1994
[3] Ahn V., Angulo J. M., Ruiz-Medina M. D., “Possible long-range dependence in fractional random fields”, J. Statist. Plann. Inference, 80 (1999), 95–110 | DOI | MR
[4] Ahn V., Leonenko N. N., Sakhno L. M., “On a class of minimum contrast estimators for fractional stochastic processes and fields”, J. Statist. Plann. Inference, 123 (2004), 161–185 | DOI | MR
[5] Ahn V., Leonenko N. N., Sakhno L. M., “Minimum contrast estimation of random processes based on information of second and third orders”, J. Statist. Plann. Inference, 137 (2007), 1302–1331 | DOI | MR
[6] Antoniadis A., Gijbels I., “Detecting abrupt changes by wavelet methods”, J. Nonparamet. Stat., 14:1–2 (2002), 7–29 | DOI | MR | Zbl
[7] Avram F., Brown L., “A generalized Hölder inequality and a generalized Szego theorem”, Proc. Amer. Math. Soc., 107:3 (1989), 687–695 | MR | Zbl
[8] Avram F., Leonenko N., Sakhno L., “On a Szegö type limit theorem, the Hölder–Young–Brascamp–Lieb inequality and the asymptotic theory of integrals and quadratic forms of stationary fields”, ESAIM Probab. Stat., 14 (2010), 210–255 | DOI | MR | Zbl
[9] Chan G., Wood A. T. A., “Estimation of fractal dimension for a class of non-Gaussian stationary processes and fields”, Ann. Statist., 32:3 (2004), 1222–1260 | DOI | MR | Zbl
[10] Corcuera J. M., Nualart D., Woerner J. H. C., “Convergence of certain functionals of integral fractional processes”, J. Theoret. Probab., 22:4 (2009), 856–870 | DOI | MR | Zbl
[11] Dahlhaus R., Künsch H., “Edge effects and efficient parameter estimation for stationary random fields”, Biometrika, 74:4 (1987), 877–882 | DOI | MR | Zbl
[12] Du J., Zhang H., Mandrekar V. S., “Fixed-domain asymptotic properties of typed maximum likelihood estimators”, Ann. Statist., 37:6A (2009), 3330–3361 | MR | Zbl
[13] Fay G., Moulines E., Roueff F., Taqqu M. S., “Estimators of long-memory: Fourier versus wavelets”, J. Econometrics, 15:2 (2009), 159–177 | DOI | MR
[14] Gao J., Ahn V., Heyde C., “Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency”, Stochastic Process. Appl., 99:2 (2002), 295–321 | DOI | MR | Zbl
[15] Giraitis L., Taqqu M. S., “Central limit theorems for quadratic forms with time domain conditions”, Ann. Probab., 26:1 (1998), 377–398 | DOI | MR | Zbl
[16] Guyon X., “Parameter estimation for a stationary process on a $d$-dimensional lattice”, Biometrika, 69:1 (1982), 95–105 | MR | Zbl
[17] Guyon X., Random Fields on a Network: Modelling, Statistics and Applications, Springer-Verlag, New York, 1995, 225 pp. | MR | Zbl
[18] Heyde C. C., Quasi-likelihood and its Applications. A General Approach to Optimal Parameter Estimation, Springer-Verlag, New York, 1997, 235 pp. | MR | Zbl
[19] Ivanov A. V., Leonenko N. N., Ruiz-Medina M. D., Savich I. N., “Limit theorems for weighted nonlinear transformations of Gaussian processes with singular spectra”, Ann. Probab., 41:2 (2013), 1088–1114 | DOI | MR | Zbl
[20] Leonenko N. N., Sakhno L. M., “On the Whittle estimators for some classes of continuous-parameter random processes and fields”, Statist. Probab. Lett., 76:8 (2003), 781–795 | DOI | MR
[21] Lim Ch. Y., Stein M. L., “Properties of spatial cross-periodograms using fixed-domain asymptotics”, J. Multivatiate Anal., 99:9 (2008), 1962–1984 | DOI | MR | Zbl
[22] Ludeña C., “Parametric estimation for Gaussian long-range dependent processes based on the log-periodogram”, Bernoulli, 6:4 (2000), 709–728 | DOI | MR | Zbl
[23] Mallat S., Hwang W. L., “Singularity detection and processing with wavelets”, IEEE Trans. Inform. Theory, 38:2 (1992), 617–643 | DOI | MR | Zbl
[24] Nason G. P., Silverman B. W., “The stationary wavelet transform and some statistical applications”, Lecture Notes in Statist., 103 (1994), 281–300 | DOI
[25] Nason G. P., von Sachs R., Kroisandt G., “Wavelet processes and adaptive estimation of evolutionary wavelet spectrum”, J. Royal Statist. Soc., Ser. B, 62 (2000), 271–292 | DOI | MR
[26] Nourdin I., Nualart D., “Central limit theorems for multiple Skorokhod integrals”, J. Theoret. Probab., 23:1 (2010), 39–64 | DOI | MR | Zbl
[27] Nualart D., The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995, 266 pp. | MR
[28] Nualart D., Ortiz-Latorre S., “Central limit theorems for multiple stochastic integrals and Malliavin calculus”, Stochastic Process. Appl., 118:4 (2008), 614–628 | DOI | MR | Zbl
[29] Nualart D., Peccati G., “Central limit theorems for sequences of multiple stochastic integrals”, Ann. Probab, 33:1 (2005), 91–115 | DOI | MR
[30] Peccati G., Tudor C. A., “Gaussian limits for vector-valued multiple stochastic integrals”, Séminaire de Probabilités XXXVIII, Lecture Notes in Math., 1857, Springer, Berlin, 2005, 247–262 | MR | Zbl
[31] Peccati G., Taqqu M. S., “Stable convergence of multiple {W}iener–{I}tô integrals”, J. Theoret. Probab., 21 (2008), 527–570 | DOI | MR | Zbl
[32] Peccati G., Taqqu M. S., “Limit theorems for multiple stochastic integrals”, ALEA Lat. Amer. J. Probab. Math. Statist., 4 (2008), 393–413 | MR | Zbl
[33] Peccati G., Taqqu M. S., “Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning”, Electron. J. Probab., 12:15 (2007), 447–480 | MR | Zbl
[34] Roueff F., Taqqu M. S., “Asymptotic normality of wavelet estimation of the memory parameter for linear processes”, J. Time Series Anal., 30:5 (2009), 534–558 | DOI | MR | Zbl
[35] Ruiz-Medina M. D., Angulo J. M., Anh V. V., “Fractional generalized random fields on bounded domains”, Stochastic Anal. Appl., 21:2 (2003), 465–492 | DOI | MR | Zbl
[36] Ruiz-Medina M. D., Crujeiras R. M., “Minimum contrast parameter estimation for fractal random fields based on the wavelet periodogram”, Comm. Statist. Theory Methods, 40:19–20 (2011), 3599–3613 | DOI | MR | Zbl
[37] Stein M. L., “Fixed-domain asymptotics for spatial periodograms”, J. Amer. Statist. Assoc., 432 (1995), 1277–1288 | DOI | MR | Zbl
[38] Surgailis D., “Long-range dependence and Appell rank”, Ann. Probab., 28:1 (2000), 478–497 | DOI | MR | Zbl
[39] Taniguchi M., “Minimum contrast estimation for spectral densities of stationary processes”, J. Roy. Statist. Soc., Ser. B, 49:3 (1987), 315–325 | MR | Zbl
[40] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland Publishing Co., Amsterdam–New York, 1978, 528 pp. | MR | Zbl
[41] Vakhania N. N., Tarieladze V. I., Chobanyan S. A., Probability Distributions on Banach Spaces, D. Reidel Publishing Co., Dordrecht, 1987, 482 pp. | MR