A CENTRAL LIMIT RESULT IN THE WAVELET DOMAIN FOR MINIMUM CONTRAST ESTIMATION OF FRACTAL RANDOM FIELDS

作者：Ruiz Medina M D^*; Crujeiras R M

来源：Theory of Probability and Its Applications, 2014, 58(3): 458-486.

DOI：10.1137/S0040585X97986679

• asymptotic normality
• minimum contrast estimator
• wavelet domain
• Wiener chaos
• stochastic differential equations
• local times
• generalized drift
• reflection
• absorption
• nonexistence of solutions

A minimum contrast criterion for consistently estimating the spatial fractal dimension in the wavelet domain is presented in [M. D. Ruiz-Medina and R. M. Crujeiras, Comm. Statist. Theory Methods., 40 (2011), pp. 3599-3613] for a class of semiparametric fractal Gaussian random fields, which includes fractional Brownian motion and Riesz-Bessel motion as particular cases. In this work, asymptotic normality of this minimum contrast estimator is obtained using central limit results for multiple stochastic integrals (see [ N. Nualart and G. Peccati, Ann. Probab., 33 (2005), pp. 91-115]).

• 出版日期2014