Estimating Functionals of a Stochastic Process
| Autor: | Jacques Istas, Catherine Laredo |
|---|---|
| Přispěvatelé: | Unité de biométrie et intelligence artificielle de jouy, Institut National de la Recherche Agronomique (INRA) |
| Rok vydání: | 1997 |
| Předmět: |
Statistics and Probability
Mathematical optimization Smoothness (probability theory) Mean squared error Stochastic process [SDV]Life Sciences [q-bio] Applied Mathematics 010102 general mathematics Estimator Hölder condition 01 natural sciences Root mean square 010104 statistics & probability Rate of convergence Applied mathematics 0101 mathematics Finite set Mathematics |
| Zdroj: | Advances in Applied Probability Advances in Applied Probability, Applied Probability Trust, 1997, 29, pp.249-270 |
| ISSN: | 1475-6064 0001-8678 |
| DOI: | 10.1017/s0001867800027877 |
| Popis: | The problem of estimating the integral of a stochastic process from observations at a finite number N of sampling points has been considered by various authors. Recently, Benhenni and Cambanis (1992) studied this problem for processes with mean 0 and Hölder index K + ½, K ; ℕ These results are here extended to processes with arbitrary Hölder index. The estimators built here are linear in the observations and do not require the a priori knowledge of the smoothness of the process. If the process satisfies a Hölder condition with index s in quadratic mean, we prove that the rate of convergence of the mean square error is N 2s+1 as N goes to ∞, and build estimators that achieve this rate. |
| Databáze: | OpenAIRE |
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