title: A multivariate generalized Cp and surface estimation.
abstract: We propose a new multivariate generalized Cp (MGCp) criterion for tuning parameter selection in nonparametric regression, applicable when there are multiple covariates whose values may be irregularly spaced. Apart from an asymptotically negligible remainder, the MGCp criterion has expected value equal to the sum of squared errors of a fitted derivative (rather than of a fitted mean response). Thus, unlike traditional criteria for tuning parameter selection, MGCp is not prone to undersmoothed derivative estimation. We illustrate a scientific application in a case study that explores the relationship among three measures of liver function. Since recent technological developments hold promise for assessing two of these measures outside of medical and laboratory facilities, better understanding of the aforementioned relationship may allow enhanced monitoring of liver function, especially in developing countries and among persons for whom access to medical and laboratory facilities is limited.
authors.affiliation: Department of Statistics, University of Kentucky, 725 Rose Street, Lexington, KY 40536, USA RJCharn2@aol.com.
authors.forename: Richard
authors.initials: R
authors.lastname: Charnigo
authors.affiliation: Department of Statistics, University of Kentucky, 725 Rose Street, Lexington, KY 40536, USA.
authors.forename: Cidambi
authors.initials: C
authors.lastname: Srinivasan
mesh_terms: D006801:Humans; D008107:Liver Diseases / Q000175:diagnosis*; D008111:Liver Function Tests / Q000706:statistics & numerical data; D015233:Models, Statistical; D015999:Multivariate Analysis; D012044:Regression Analysis; D018709:Statistics, Nonparametric
keywords: Bilirubin; Compound estimation; Curve estimation; Functional data analysis; Liver disease; Nonparametric regression; Tuning parameter