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Article Dans Une Revue Journal of Statistical Planning and Inference Année : 1986

A note on prediction via estimation of the conditional mode function

Résumé

Let (Xi, Yi) in ExR, E in Rd be a strictly stationary process. The conditional density of Y given X is estimated by the kernel method. It is shown that the (empirically determined) mode of the kernel estimate is uniformly (in a compact) convergent to the conditional mode function when the process is Φ-mixing. This result is applied to a strictly stationary time series {Zk}k∈N which is markovian of order q. It is seen that the so-called model predictor of ZN + 1 from the observed data is converging to the predictor that is based on the full knowledge of the conditional density of ZN + 1 given {Z1,…,ZN}.

Dates et versions

hal-04408305 , version 1 (21-01-2024)

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Citer

G. Collomb, W. Härdle, S. Hassani. A note on prediction via estimation of the conditional mode function. Journal of Statistical Planning and Inference, 1986, 15, pp.227-236. ⟨10.1016/0378-3758(86)90099-6⟩. ⟨hal-04408305⟩
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