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Maximum likelihood estimator in a two-phase nonlinear random regression model
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Gabriela Ciuperca
Veröffentlicht/Copyright:
25. September 2009
Summury
We consider a two-phase random design nonlinear regression model, the regression function is discontinuous at the change-point. The errors ∊ are arbitrary, with E(∊) = 0 and E(∊2) < ∞. We prove that Koul and Qian’s results [12] for linear regression still hold true for the nonlinear case. Thus the maximum likelihood estimator r^n of the change-point r is n-consistent and the estimator θ^1n of the regression parameters θ1 is n1/2-consistent. The asymptotic distribution of n1/2(θ^1n − θ01) is Gaussian and n(r^n − r) converges to the left end point of the maximizing interval with respect to the change point. The likelihood process is asymptotically equivalent to a compound Poisson process.
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Published Online: 2009-09-25
Published in Print: 2004-04-01
© R. Oldenbourg Verlag, München
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- Quantization of probability distributions under norm-based distortion measures
- Confidence estimation of the covariance function of stationary and locally stationary processes
- Efficient estimation of a linear functional of a bivariate distribution with equal, but unknown, marginals: The minimum chi-square approach
- Locally asymptotically optimal tests in semiparametric generalized linear models in the 2-sample-problem
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Artikel in diesem Heft
- Quantization of probability distributions under norm-based distortion measures
- Confidence estimation of the covariance function of stationary and locally stationary processes
- Efficient estimation of a linear functional of a bivariate distribution with equal, but unknown, marginals: The minimum chi-square approach
- Locally asymptotically optimal tests in semiparametric generalized linear models in the 2-sample-problem
- Maximum likelihood estimator in a two-phase nonlinear random regression model
