TY - JOUR
AU - Thi To Nhu, Dang
PY - 2023/06/28
Y2 - 2024/09/17
TI - Parameter Estimation for H-self-similar Stable Fields
JF - Thailand Statistician
JA - Thail. Stat.
VL - 21
IS - 3
SE - Articles
DO -
UR - https://ph02.tci-thaijo.org/index.php/thaistat/article/view/250055
SP - 484-497
AB - <p>In this work, we are interested in <img title="H" src="https://latex.codecogs.com/gif.latex?H">-sssi <img title="\alpha" src="https://latex.codecogs.com/gif.latex?\alpha">- stable fields, that is, in stable random fields that are self-similar with parameter $H$ and have stationary increments. We give two estimators of the stability and the self-similar indices based on <img title="\beta" src="https://latex.codecogs.com/gif.latex?\beta">-negative power variations with <img title="-1/2<\beta<0." src="https://latex.codecogs.com/gif.latex?-1/2<\beta<0."> The consistency of those two estimators are also proved. We illustrate these convergences with some examples: Levy fractional Brownian field, well-balanced linear fractional stable field and Takenaka random field.</p>
ER -