Global smoothness estimation of a Gaussian process from general sequence designs

作者：Blanke Delphine^*; Vial Celine

来源：Electronic Journal of Statistics, 2014, 8(1): 1152-1187.

DOI：10.1214/14-EJS925

• Inference for Gaussian processes
• locally stationary process
• divided differences
• quadratic variations
• unevenly spaced data

`We consider a real Gaussian process X with global unknown smoothness (r(0), beta(0)): more precisely X-(r0), r(0) is an element of N-0, is supposed to be locally stationary with Holder exponent beta(0), beta(0) is an element of]0, 1[. For X observed at a finite set of points, we derive estimators of r(0) and beta(0) based on the quadratic variations for the divided differences of X. Under mild conditions, we obtain an exponential bound for estimating r(0), as well as sharp rates of convergence (up to logarithmic factors) for the estimation of beta(0). An extensive simulation study illustrates the finite-sample properties of both estimators for different types of processes and we also include two real data applications.

• 出版日期2014