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M-estimates for stationary and scaled residuals
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Christopher S. Withers
Veröffentlicht/Copyright:
7. Dezember 2007
Suppose we have observations Yt = mt(θ) + et in ℝ for t = 1, 2, …, n where each mt = mt(θ) is a smooth function of an unknown vector θ, and the noise {et} is stationary with unknown marginals. We obtain asymptotic normality of the M-estimate θ with respect to any suitable smooth function ρ(e). Hence we obtain confidence regions for any smooth vector function t(θ) with ∂t(θ)/∂θ' of full rank. Extensions are given to the model Yt = mt(θ) + σt(θ)et in ℝ. Heuristic proofs are given.
Received: 2006-November-12
Revised: 2007-May-03
Published Online: 2007-12-07
Published in Print: 2007-10-19
© de Gruyter 2007
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Artikel in diesem Heft
- Approximation of random dynamical systems with discrete time by stochastic differential equations: I. Theory
- Two-boundary problems for semi-Markov walk with a linear drift
- Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension
- Weak solutions and a Yamada–Watanabe theorem for FBSDEs
- M-estimates for stationary and scaled residuals
- A simple formula for parabolic cylinder functions
- Correction on a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition
Schlagwörter für diesen Artikel
Asymptotic normality;
M-estimates;
smooth functions;
stationary and scaled residuals
Artikel in diesem Heft
- Approximation of random dynamical systems with discrete time by stochastic differential equations: I. Theory
- Two-boundary problems for semi-Markov walk with a linear drift
- Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension
- Weak solutions and a Yamada–Watanabe theorem for FBSDEs
- M-estimates for stationary and scaled residuals
- A simple formula for parabolic cylinder functions
- Correction on a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition
