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Some statistical properties of the kernel-diffeomorphism estimator

The kernel density estimation method is not so attractive when the density has its support confined to a bounded space U of R d . In a recent paper, we suggested a new nonparametric probability density function (p.d.f.) estimator called the 'kernel-diffeomorphism estimator', which suppressed border convergence difficulties by using an appropriate regular change of variable. The present paper gives more asymptotic theory (uniform consistency, normality). An invariance criterion for p.d.f. estimators is discussed. The invariance of the kernel diffeomorphism estimator under special affine motion (a translation followed by any member of the special linear group SL(d, R)) is proved.