In order to construct confidence sets for a marginal density f of a strictly stationary continuous time process observed over the time interval [0, T ], it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator f T . In this paper we address the question of n
Asymptotics for Lp-norms of kernel estimators of densities
✍ Scribed by Miklós Csörgő; Lajos Horváth
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 605 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0167-9473
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📜 SIMILAR VOLUMES
In this paper, we build a central limit theorem for triangular arrays of sequences which satisfy a mild mixing condition. This result allows us to study asymptotic normality of density kernel estimators for some classes of continuous and discrete time processes.
Let (X 1 , Y 1 ), (X 2 , Y 2 ), ..., be d+1 dimensional random vectors which are distributed as (X, Y). Let %(x) be the conditional median, that is, We consider the problem of estimating %(x) from the data (X 1 , Y 1 ), ..., (X n , Y n ) which are :-mixing dependence. L 1 -norm kernel estimators of