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Estimation of Knots in Linear Spline Models

The linear spline model is able to accommodate nonlinear effects while allowing for an easy interpretation. It has significant applications in studying threshold effects and change-points. However, its application in practice has been limited by the lack of both rigorously studied and computationally convenient method for estimating knots. A key difficulty in estimating knots lies in the nondifferentiability. In this article, we study influence functions of regular and asymptotically linear estimators for linear spline models using the semiparametric theory. Based on the theoretical development, we propose a simple semismooth estimating equation approach to circumvent the nondifferentiability issue using modified derivatives, in contrast to the previous smoothing-based methods. Without relying on any smoothing parameters, the proposed method is computationally convenient. To further improve numerical stability, a two-step algorithm taking advantage of the analytic solution available when knots are known is developed to solve the proposed estimating equation. Consistency and asymptotic normality are rigorously derived using the empirical process theory. Simulation studies have shown that the two-step algorithm performs well in terms of both statistical and computational properties and improves over existing methods. Supplementary materials for this article are available online.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.118 No.541 March 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 639-650

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

EFFICIENCY
CHANGE-POINT
DIFFERENTIABLE IN QUADRATIC MEAN
GRADIENT-DESCENT
SEMIPARAMETRIC SEMISMOOTH ESTIMATING EQUATION

Info Detail Spesifik

https://doi.org/10.1080/01621459.2021.1947307

Pernyataan Tanggungjawab

Guangyu Yang, Baqun Zhang, Min Zhang

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