Limiting law results for a class of conditional mode estimates for functional stationary ergodic data View Full Text


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Article Info

DATE

2016-07

AUTHORS

S. Bouzebda, M. Chaouch, N. Laïb

ABSTRACT

The main purpose of the present work is to establish the functional asymptotic normality of a class of kernel conditional mode estimates when functional stationary ergodic data are considered. More precisely, consider a random variable (X,Z) taking values in some semi-metric abstract space E × F. For a real function φ defined on F and for each x ∈ E, we consider the conditional mode, say ⊝φ(x), of the real random variable φ(Z) given the event “X = x”. While estimating the conditional mode function by Θ̂φ,n(x), using the kernel-type estimator, we establish the limiting law of the family of processes {Θ̂φ(x) - Θφ(x)} (suitably normalized) over Vapnik–Chervonenkis class C of functions φ. Beyond ergodicity, no other assumption is imposed on the data. This paper extends the scope of some previous results established under mixing condition for a fixed function φ. From this result, the asymptotic normality of a class of predictors is derived and confidence bands are constructed. Finally, a general notion of bootstrapped conditional mode constructed by exchangeably weighting samples is presented. The usefulness of this result will be illustrated in the construction of confidence bands. More... »

PAGES

168-195

References to SciGraph publications

  • 1997. Probability Theory, Independence, Interchangeability, Martingales in NONE
  • 2006-05. Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models in STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES
  • 2002. Foundations of Modern Probability in NONE
  • 2012. Inference for Functional Data with Applications in NONE
  • 1985. Exchangeability and related topics in ÉCOLE D'ÉTÉ DE PROBABILITÉS DE SAINT-FLOUR XIII — 1983
  • 2005-09. Resampling student'st-type statistics in ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
  • 2013-04. Degenerate - and -statistics under ergodicity: asymptotics, bootstrap and applications in statistics in ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
  • 2017-03. Rate of uniform consistency for a class of mode regression on functional stationary ergodic data in STATISTICAL METHODS & APPLICATIONS
  • 1995. The Jackknife and Bootstrap in NONE
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    43 schema:description The main purpose of the present work is to establish the functional asymptotic normality of a class of kernel conditional mode estimates when functional stationary ergodic data are considered. More precisely, consider a random variable (X,Z) taking values in some semi-metric abstract space E × F. For a real function φ defined on F and for each x ∈ E, we consider the conditional mode, say ⊝φ(x), of the real random variable φ(Z) given the event “X = x”. While estimating the conditional mode function by Θ̂φ,n(x), using the kernel-type estimator, we establish the limiting law of the family of processes {Θ̂φ(x) - Θφ(x)} (suitably normalized) over Vapnik–Chervonenkis class C of functions φ. Beyond ergodicity, no other assumption is imposed on the data. This paper extends the scope of some previous results established under mixing condition for a fixed function φ. From this result, the asymptotic normality of a class of predictors is derived and confidence bands are constructed. Finally, a general notion of bootstrapped conditional mode constructed by exchangeably weighting samples is presented. The usefulness of this result will be illustrated in the construction of confidence bands.
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