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Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data

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  • Said Attaoui

Abstract

In this paper, we investigate a nonparametric estimation of the conditional density of a scalar response variable given a random variable taking values in separable Hilbert space. We establish under general conditions the uniform almost complete convergence rates and the asymptotic normality of the conditional density kernel estimator, when the variables satisfy the strong mixing dependency, based on the single-index structure. The asymptotic $$(1-\zeta )$$ ( 1 - ζ ) confidence intervals of conditional density function are given, for $$0 > \zeta > 1$$ 0 > ζ > 1 . We further demonstrate the impact of this functional parameter to the conditional mode estimate. Simulation study is also presented. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 257-286, July.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:3:p:257-286
    DOI: 10.1007/s10182-014-0227-3
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