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On a likelihood-based approach in nonparametric smoothing and cross- validation. (English) Zbl 0811.62043

Summary: A likelihood-based generalization of usual kernel and nearest neighbor- type smoothing techniques and a related extension of the least-squares leave-one-out cross-validation are explored in a generalized regression set up. Several attractive features of the procedure are discussed and asymptotic properties of the resulting nonparametric function estimate are derived under suitable regularity conditions. Large sample performance of likelihood-based leave-one-out cross validation is investigated by means of certain asymptotic expansions.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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