Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao zbMATH Openarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2020
Data sources: zbMATH Open
Statistica Sinica
Article . 2020 . Peer-reviewed
Data sources: Crossref
versions View all 2 versions
addClaim

Inference for Generalized partial functional linear regression

Inference for generalized partial functional linear regression
Authors: Li, Ting; Zhu, Zhongyi;

Inference for Generalized partial functional linear regression

Abstract

A penalized likelihood ratio test for generalized partial functional linear models is proposed. A roughness penalty is used to control the model complexity via a smoothing parameter. A new type of inner product is defined. Using this inner product, a Bahadur representation for both functional and scalar penalized estimators is developed based on the reproducing kernel Hilbert space. The proposed approach allows for detecting the significant effects of the functional and scalar covariates on the scalar outcome, either simultaneously or separately. It is shown that the scalar estimators are asymptotically independent of the estimator of the functional part. The null limit distribution of the proposed test statistic is shown to be normal and approximately chi-square. The restriction that the scalar covariates can only linearly associate with the functional process is imposed and then the decay rates of the corresponding coefficients are determined. Simulation studies are presented to investigate the finite sample performance of the model. The simulated data are generated from the partial functional linear model and the partial functional logistic regression model. An application of the model is made to determine effects of PM2.5, the functional part formed with daily concentration measurements from April 1 to August 31, 2000, in the presence of scalar factors. The response variable is the nonaccidental mortality rate across different cities in the United States measured by the log-transformed total mortality rate in the following month, September 2000, among individuals of age 65 and older. The data set is obtained from the National Mortality, Morbidity, and Air Pollution Study. Significant effects of PM2.5, proportion of the population with at least a high school diploma, proportion of the population with at least a university diploma, and proportion of the population below the poverty line are found.

Keywords

Generalized linear models (logistic models), Functional data analysis, Reliability and life testing, hypothesis testing, Bahadur representation, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Applications of statistics to environmental and related topics, penalized likelihood ratio test, reproducing kernel Hilbert space, Applications of statistics to biology and medical sciences; meta analysis

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!