Abstract
We consider a change-point problem in regression estimation. Observations (X i , Y i ), i = 1, ..., n, are governed by the model Y i = m(X i ) + σ(X i )ɛ i , where the (ɛ i )i∈ℤ are independent and identically distributed and independent of (X i )i∈ℤ. The latter sequence satisfies a weak dependence condition proposed by Dedecker and Prieur [4]. We essentially study the basic situation, where the regression function has a unique change point. The construction of the jump estimate process, t → \(\hat \gamma \)(t), is based on local linear regression. Under a positivity condition regarding the asymmetric kernel involved, we prove the convergence of a local dilated-rescaled version of \(\hat \gamma \)(t) to a compound Poisson process with an additional drift. We also derive asymptotic normality results.
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Prieur, C. Change point estimation by local linear smoothing under a weak dependence condition. Math. Meth. Stat. 16, 25–41 (2007). https://doi.org/10.3103/S1066530707010036
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DOI: https://doi.org/10.3103/S1066530707010036
Key words
- central limit theorem
- change point
- infinitely divisible distributions
- Lindeberg theorem
- local linear regression
- nonparametric regression
- stationary sequences
- weakly dependent sequences