The S-estimator in the change-point random model with long memory

Ciuperca, Gabriela

doi:10.1080/02331888.2011.553683

Cited by 2 publications

(2 citation statements)

References 48 publications

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“…An annotated bibliography by Khodadadi and Asgharian (2008) includes many of the articles pertinent to our research interest. Ciuperca (2009) has more recent citations in the introduction of his article. The model we study is a small but useful subset of the "regime(d)" regression, a phrase first used by Quandt (1958) in economic literature, or more currently referred to as a broken-line regression (Gill, 2004).…”

Section: Introductionmentioning

confidence: 96%

Estimation of Parameters in the Joinpoint Two-Regime Regression Model

Hoffman

Knofczynski

Clark

2010

Communications in Statistics - Simulation and Computation

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Of interest is the specific model called the joinpoint two-regime regression or broken line model composed of one regression line and a horizontal ray. This is a very restricted but highly useful subset of the well-researched change point problem. The usual approach, first presented by Quandt (1958), is to find estimates of the slope, intercept, and joinpoint by assuming that the error terms are generated from a normal distribution. For our specific model this method of estimation was shown by Gill (2004) to produce the maximum likelihood estimates. We develop a method that does not rely on the assumption of normal, independent, identically distributed (iid) error terms. We illustrate the method by applying it to proximity indexes of whale cow and calf pairs, and compare our new method to the Quandt estimates in a simulation study showing our new method performs adequately in the normal iid error term model and is preferable in small samples where error terms are correlated with non constant variance.

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Section: Introductionmentioning

confidence: 96%

Estimation of Parameters in the Joinpoint Two-Regime Regression Model

Hoffman

Knofczynski

Clark

2010

Communications in Statistics - Simulation and Computation

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“…Several examples for change point models in regression analysis are considered in [9][10][11][12][13][14][15][16][17][18][19] and the cited references therein. In Csörgö and Horváth [20] and Kosorok [4,Chapter 14.5.1] locating a jump discontinuity is considered and properties of the estimators are studied.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric cusp estimation in regression models

Döring

2015

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We consider the problem of estimating the location of an asymmetric cusp θ 0 in a regression model. That means, we focus on regression functions, which are continuous at θ 0 , but the degree of smoothness from the left p 0 could be different to the degree of smoothness from the right q 0 . The degrees of smoothness have to be estimated as well. We investigate the consistency with increasing sample size n of the leastsquares estimates. It turns out that the rates of convergence ofθ n depend on the minimum b of p 0 and q 0 and that our estimator converges to a maximizer of a Gaussian process. In the regular case, that is, for b greater than 1 2 , we have a rate of √ n and the asymptotic normality property. In the non-regular case, we have a representation of the limit distribution ofθ n as maximizer of a fractional Brownian motion with drift.

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The S-estimator in the change-point random model with long memory

Cited by 2 publications

References 48 publications

Estimation of Parameters in the Joinpoint Two-Regime Regression Model

Estimation of Parameters in the Joinpoint Two-Regime Regression Model

Asymmetric cusp estimation in regression models

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