Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties...

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Published inMathematics (Basel) Vol. 10; no. 19; p. 3433
Main Authors DIDI, Sultana, AL HARBY, Ahoud AL, BOUZEBDA, Salim
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2022
MDPI
Subjects
Asymptotic methods
Asymptotic properties
Density
Discriminant analysis
Ergodic processes
ergodicity
Estimation theory
Estimators
Functional Analysis
Functionals
Hilbert space
Martingales
Mathematical functions
Mathematics
multivariate density estimation
multivariate regression estimation
Probability
Random variables
rates of strong convergence
Regression
Regression analysis
stationarity
Stationary processes
Statistics
Statistics Theory
Wavelet transforms
wavelet-based estimators
Saudi Arabia
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Abstract The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values.
AbstractList The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values.
Audience Academic
Author AL HARBY, Ahoud AL
BOUZEBDA, Salim
DIDI, Sultana
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  surname: AL HARBY
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  givenname: Salim
  orcidid: 0000-0001-7801-4945
  surname: BOUZEBDA
  fullname: BOUZEBDA, Salim
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SubjectTerms Asymptotic methods
Asymptotic properties
Density
Discriminant analysis
Ergodic processes
ergodicity
Estimation theory
Estimators
Functional Analysis
Functionals
Hilbert space
Martingales
Mathematical functions
Mathematics
multivariate density estimation
multivariate regression estimation
Probability
Random variables
rates of strong convergence
Regression
Regression analysis
stationarity
Stationary processes
Statistics
Statistics Theory
Wavelet transforms
wavelet-based estimators
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Title Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time
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