A smooth simultaneous confidence band for correlation curve
ZHANG, Yuanyuan - Personal Name
YANG, Lijian - Personal Name
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 cor-
relation 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. Simu-
lated 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).
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 cor-
relation 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. Simu-
lated 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).
Availability
| EB00000004114K | Available |
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E-Jurnal
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Subject(s)
Confidence band
Correlation curve
Heteroscedasticity
Infeasible estimator
Local quadratic estimator
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Statement of Responsibility
Yuanyuan Zhang 1, Lijian Yang 1
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