A maximal inequality for continuous martingales and \(M\)-estimation in a Gaussian white noise model

DOI10.1214/aos/1018031212zbMath0954.62100OpenAlexW1836658400MaRDI QIDQ1970485

Yoichi Nishiyama

Publication date: 30 January 2001

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1018031212

zbMATH Keywords

Gaussian white noiseM-estimation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Gaussian processes (60G15) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Non-Markovian processes: estimation (62M09) Martingales with continuous parameter (60G44)

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Weak convergence of some classes of martingales with jumps., Asymptotically distribution free test for parameter change in a diffusion process model, Deterministic equivalents of additive functionals of recurrent diffusions and drift estimation, Goodness of fit test for ergodic diffusions by tick time sample scheme, Goodness of fit test for ergodic diffusion processes, Regression discontinuity designs, white noise models, and minimax, Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach, On the rate of convergence of the maximum likelihood estimator in Brownian semimartingale models, Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions, Asymptotic theory of semiparametric \(Z\)-estimators for stochastic processes with applications to ergodic diffusions and time series, Donsker theorems for diffusions: necessary and sufficient conditions

Cites Work

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• Asymptotic behavior of M-estimator and related random field for diffusion process
• Cube root asymptotics
• Estimating a regression function
• Estimating a density under order restrictions: Nonasymptotic minimax risk
• Estimation for diffusion processes from discrete observation
• Kernel-type estimators of jump points and values of a regression function
• Rates of convergence for minimum contrast estimators
• Some central limit theorems for \(\ell^\infty\)-valued semimartingales and their applications
• Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
• The method of sieves and minimum contrast estimators
• Weak convergence and empirical processes. With applications to statistics
• Hellinger-consistency of certain nonparametric maximum likelihood estimators
• Estimation of the mode
• On Minimax Estimation of a Discontinuous Signal
• Minimum contrast estimation in diffusion processes
• Jump and sharp cusp detection by wavelets