scholarly journals Estimation for Functional Single Index Models with Unknown Link Functions

2023 ◽  
Author(s):  
Yunxiang Huang ◽  
Qihua Wang
2019 ◽  
Vol 09 (02) ◽  
pp. 2150005
Author(s):  
Jian-Qiang Zhao ◽  
Yan-Yong Zhao ◽  
Jin-Guan Lin ◽  
Zhang-Xiao Miao ◽  
Waled Khaled

We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.


Biometrika ◽  
2021 ◽  
Author(s):  
Yifei Sun ◽  
Sy Han Chiou ◽  
Kieren A Marr ◽  
Chiung-Yu Huang

Abstract Single-index models have gained increased popularity in time-to-event analysis owing to their model flexibility and advantage in dimension reduction. In this paper, we propose a semiparametric framework for the rate function of a recurrent event counting process by modelling its size and shape components with single-index models. With additional monotone constraints on the two link functions for the size and shape components, the proposed model possesses the desired directional interpretability of covariate effects and encompasses many commonly used models as special cases. To tackle the analytical challenges arising from leaving the two link functions unspecified, we develop a two-step rank-based estimation procedure to estimate the regression parameters with or without informative censoring. The proposed estimators are asymptotically normal, with a root-n convergence rate. To guide model selection, we develop hypothesis testing procedures for checking shape- and size-independence. Simulation studies and a data example on a hematopoietic stem cell transplantation study are presented to illustrate the proposed methodology.


Author(s):  
Takayuki Iguchi ◽  
Andrés F. Barrientos ◽  
Eric Chicken ◽  
Debajyoti Sinha

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