Local regression for vector responses

A. H. Welsh*, T. W. Yee

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    35 Citations (Scopus)

    Abstract

    We explore a class of vector smoothers based on local polynomial regression for fitting nonparametric regression models which have a vector response. The asymptotic bias and variance for the class of estimators are derived for two different ways of representing the variance matrices within both a seemingly unrelated regression and a vector measurement error framework. We show that the asymptotic behaviour of the estimators is different in these four cases. In addition, the placement of the kernel weights in weighted least squares estimators is very important in the seeming unrelated regressions problem (to ensure that the estimator is asymptotically unbiased) but not in the vector measurement error model. It is shown that the component estimators are asymptotically uncorrelated in the seemingly unrelated regressions model but asymptotically correlated in the vector measurement error model. These new and interesting results extend our understanding of the problem of smoothing dependent data.

    Original languageEnglish
    Pages (from-to)3007-3031
    Number of pages25
    JournalJournal of Statistical Planning and Inference
    Volume136
    Issue number9
    DOIs
    Publication statusPublished - 1 Sept 2006

    Fingerprint

    Dive into the research topics of 'Local regression for vector responses'. Together they form a unique fingerprint.

    Cite this