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• W2053778794 abstract "We consider a real Gaussian process $X$ with global unknown smoothness $(r_{scriptscriptstyle 0},beta _{scriptscriptstyle 0}$): more precisely $X^{(r_{scriptscriptstyle 0})}$, $r_{scriptscriptstyle 0}in{mathds {N}}_{0}$, is supposed to be locally stationary with Hölder exponent $beta _{scriptscriptstyle 0}$, $beta _{scriptscriptstyle 0}in]0,1[$. For $X$ observed at a finite set of points, we derive estimators of $r_{scriptscriptstyle 0}$ and $beta _{scriptscriptstyle 0}$ based on the quadratic variations for the divided differences of $X$. Under mild conditions, we obtain an exponential bound for estimating $r_{scriptscriptstyle 0}$, as well as sharp rates of convergence (up to logarithmic factors) for the estimation of $beta _{scriptscriptstyle 0}$. 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." @default.
• W2053778794 created "2016-06-24" @default.
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• W2053778794 date "2014-01-01" @default.
• W2053778794 modified "2023-09-30" @default.
• W2053778794 title "Global smoothness estimation of a Gaussian process from general sequence designs" @default.
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• W2053778794 doi "https://doi.org/10.1214/14-ejs925" @default.
• W2053778794 hasPublicationYear "2014" @default.
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