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Jump detection in single-index models with measurement error

Author

Listed:
  • Liu, Yuan
  • Zhao, Yan-Yong
  • Ismail, Noriszura
  • Tajuddin, Razik Ridzuan Mohd
  • Zhang, Yuchun

Abstract

Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.

Suggested Citation

  • Liu, Yuan & Zhao, Yan-Yong & Ismail, Noriszura & Tajuddin, Razik Ridzuan Mohd & Zhang, Yuchun, 2026. "Jump detection in single-index models with measurement error," Journal of Multivariate Analysis, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:jmvana:v:212:y:2026:i:c:s0047259x25001691
    DOI: 10.1016/j.jmva.2025.105574
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    References listed on IDEAS

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