×

Semiparametric jump-detection-based estimation for single-index models with jumps. (Chinese. English summary) Zbl 1499.62147

Summary: Single-index models are common dimension reduction models in statistics. In practical applications, the link function may have singularities, including jumps at some unknown positions and structural changes of the related process. Detection of such singularities is important for estimating the coefficients and understanding the structural changes. This article proposes a jump detection method based on the refined minimum average conditional variance estimation and zero-crossing properties of second-order derivative of a function. Using the detected jumps, we give semiparametric jump-detection-based estimators for the parameter vector and the link function. Then the selection of procedure parameters is discussed. Under some mild conditions, we establish large sample properties of the jump detection procedure and the proposed estimators. Numerical studies and a real data analysis are conducted to assess the finite sample property of the proposed methods.

MSC:

62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
PDFBibTeX XMLCite
Full Text: DOI