Estimation for a hybrid model of functional and linear measurement errors regression with missing response.
- Resource Type
- Article
- Authors
- Zou, Yuye; Wu, Chengxin; Fan, Guoliang; Zhang, Riquan
- Source
- Statistics. Apr2022, Vol. 56 Issue 2, p271-296. 26p.
- Subject
- *MEASUREMENT errors
*MISSING data (Statistics)
*LENGTH measurement
*MAXIMUM likelihood statistics
*CHI-square distribution
*ASYMPTOTIC distribution
*LEAST squares
- Language
- ISSN
- 0233-1888
In this paper, we consider least squares estimation and empirical likelihood inference for partial functional linear models when the covariates in the non-functional linear component are measured with additive error and the responses are missing at random. Asymptotic properties of the proposed estimators for the parametric and nonparametric components are established. A class of empirical log-likelihood ratio functions of the parametric component and response mean are developed, and the corresponding maximum empirical likelihood estimators are constructed. We also prove that the empirical log-likelihood ratio functions are asymptotic standard chi-squared distribution. The results can be used to construct confidence intervals for the parametric component and response mean. The asymptotic distributions of the corresponding maximum empirical likelihood estimators are also established. Meanwhile, a simulation study is conducted to demonstrate the finite sample performance of the proposed procedure. A real data analysis is also used to illustrate our methods. [ABSTRACT FROM AUTHOR]