The M-estimator in a multi-phase random nonlinear model

2007/06/01 by Gabriela Ciuperca, Ciuperca, Gabriela
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Applied mathematics #Distribution (mathematics) #Estimator #FOS: Computer and information sciences #FOS: Mathematics #Gaussian #Mathematical analysis #Mathematics #Methodology (stat.ME) #Nonlinear regression #Optimal Experimental Design Methods #Physics #Poisson distribution #Poisson regression #Population #Probability (math.PR) #Regression analysis #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #math.PR #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.0706.0153

19 pages

openalex publication_date 2007/06/01 · arxiv created 2008/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error ε. In the case when the number of jumps is known, the M-estimator of locations of breaks and of regression parameters are studied. These estimators are consistent and the distribution of the regression parameter estimators is Gaussian. The estimator of each change-point converges, with the rate n^-1, to the smallest minimizer of the independent compound Poisson processes. The results are valid for a large class of error distributions.

Citations

• Estimating and Testing Linear Models with Multiple Structural Changes
• Robust Estimation of a Location Parameter

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