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A smooth simultaneous confidence band for correlation curve

Yuanyuan Zhang and Lijian Yang ()
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Yuanyuan Zhang: Tsinghua University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 2, 247-269

Abstract: Abstract A plug-in estimator is proposed for a local measure of variance explained by regression, termed correlation curve in Doksum et al. (J Am Stat Assoc 89:571–582, 1994), consisting of a two-step spline–kernel estimator of the conditional variance function and local quadratic estimator of first derivative of the mean function. The estimator is oracally efficient in the sense that it is as efficient as an infeasible correlation estimator with the variance function known. As a consequence of the oracle efficiency, a smooth simultaneous confidence band (SCB) is constructed around the proposed correlation curve estimator and shown to be asymptotically correct. Simulated examples illustrate the versatility of the proposed oracle SCB which confirms the asymptotic theory. Application to a 1995 British Family Expenditure Survey data has found marginally significant evidence for a local version of Engel’s law, i.e., food budget share and household real income are inversely related (Hamilton in Am Econ Rev 91:619–630, 2001).

Keywords: Confidence band; Correlation curve; Heteroscedasticity; Infeasible estimator; Local quadratic estimator; 62G05; 62G08; 62G10; 62G15; 62G20; 62P20 (search for similar items in EconPapers)
Date: 2018
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