Smoothing and preservation of irregularities using local linear fitting

Gijbels, Irène

doi:10.1007/s10492-008-0003-3

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…A useful distinction (Hansen, ) can be made between two subclasses of change point models: change‐point models and threshold models. In a change‐point model (e.g., Muller, ; Loader et al, ; Csörgö and Horváth, ; Zeileis et al, ; Antoch et al, ; Gijbels, ) the samples have a natural order based on, for example, time or position on a chromosome. Change‐point models are often used to detect structural changes along the natural axis.…”

Section: Introductionmentioning

confidence: 99%

Model-Robust Inference for Continuous Threshold Regression Models

Fong

Huang

et al. 2016

Biometrics

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Summary We study threshold regression models that allow the relationship between the outcome and a covariate of interest to change across a threshold value in the covariate. In particular we focus on continuous threshold models, which experience no jump at the threshold. Continuous threshold regression functions can provide a useful summary of the association between outcome and the covariate of interest, because they offer a balance between flexibility and simplicity. Motivated by collaborative works in studying immune response biomarkers of transmission of infectious diseases, we study estimation of continuous threshold models in this paper with particular attention to inference under model misspecification. We derive the limiting distribution of the maximum likelihood estimator, and propose both Wald and test-inversion confidence intervals. We evaluate finite sample performance of our methods, compare them with bootstrap confidence intervals, and provide guidelines for practitioners to choose the most appropriate method in real data analysis. We illustrate the application of our methods with examples from the HIV-1 immune correlates studies.

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