A simultaneous confidence corridor for varying coefficient regression with sparse functional data

Lijie Gu, Li Wang, Wolfgang Härdle and Lijian Yang

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2014, vol. 23, issue 4, 806-843

Abstract: We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time-independent covariates with coefficients as functions of time-dependent covariates. Based on spline smoothing, we propose data-driven simultaneous confidence corridors for the coefficient functions with asymptotically correct confidence level. Such confidence corridors are useful benchmarks for statistical inference on the global shapes of coefficient functions under any hypotheses. Simulation experiments corroborate with the theoretical results. An example in CD4/HIV study is used to illustrate how inference is made with computable p values on the effects of smoking, pre-infection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment. Copyright Sociedad de Estadística e Investigación Operativa 2014

Keywords: B spline; Confidence corridor; Karhunen–Loève $$L^{2}$$ L 2 representation; Knots; Functional data; Varying coefficient; 62G08; 62G15; 62G32 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:23:y:2014:i:4:p:806-843

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DOI: 10.1007/s11749-014-0392-4

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