Kernel spatial density estimation in infinite dimension space

Dabo‐Niang, Sophie; Yao, Anne-Françoise

doi:10.1007/s00184-011-0374-4

Cited by 16 publications

(5 citation statements)

References 40 publications

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“…for some C > 0, and some κ ≥ 1. Such functions ψ(n, m) can be found, for instance, in Tran (1990), Carbon et al (1997), Hallin et al (2004), Biau & Cadre (2004), Dabo-Niang & Yao (2013).…”

Section: Large Sample Properties and Assumptionsmentioning

confidence: 97%

Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

Ndiaye

Dabo‐Niang

Ngom

2022

Rev. colomb. estad.

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In this work, we consider a nonparametric prediction of a spatiofunctional process observed under a non-random sampling design. The proposed predictor is based on functional regression and depends on two kernels, one of which controls the spatial structure and the other measures the proximity between the functional observations. It can be considered, in particular, as a supervised classification method when the variable of interest belongs to a predefined discrete finite set. The mean square error and almost complete (or sure) convergence are obtained when the sample considered is a locally stationary α-mixture sequence. Numerical studies were performed to illustrate the behavior of the proposed predictor. The finite sample properties based on simulated data show that the proposed prediction method outperformsthe classical predictor which not taking into account the spatial structure.

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Section: Large Sample Properties and Assumptionsmentioning

confidence: 97%

Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

Ndiaye

Dabo‐Niang

Ngom

2022

Rev. colomb. estad.

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“…Using the fact that the Hermite polynomials form an Appell sequence (see e.g. Appell, 1880) we deduce that 12) using the orthonormality of the H k 1 ,...,km with respect to ·, · g 1 . Using elementary arguments from combinatorics, we also have # (k1, .…”

Section: Proof Of Theorem 41mentioning

confidence: 99%

Nonparametric density estimation for intentionally corrupted functional data

Delaigle¹,

Meister²

2021

STAT SINICA

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We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the distribution of the original functional random variables, masked near the origin, uniquely, and we construct a nonparametric estimator of that density. We derive an upper bound for its mean integrated squared error which has a polynomial convergence rate, and we establish an asymptotic lower bound on the minimax convergence rates which is close to the rate attained by our estimator. Our estimator requires the choice of a basis and of two smoothing parameters. We propose data-driven ways of choosing them and prove that the asymptotic quality of our estimator is not significantly affected by the empirical parameter selection. We examine the numerical performance of our method via simulated examples.

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“…In the context of non-parametric estimation for spatial data, the existing papers are mostly concerned with estimating probability density and regression functions. Hence, we will cite some important references [11][12][13][14][15] and the references in which they are included. By considering the conditional Uprocesses, we give a more generic and abstract context based on this research.…”

Section: Introductionmentioning

confidence: 99%

Non-Parametric Conditional U-Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design

Bouzebda

Soukarieh

2022

Mathematics

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Stute presented the so-called conditional U-statistics generalizing the Nadaraya–Watson estimates of the regression function. Stute demonstrated their pointwise consistency and the asymptotic normality. In this paper, we extend the results to a more abstract setting. We develop an asymptotic theory of conditional U-statistics for locally stationary random fields {Xs,An:sinRn} observed at irregularly spaced locations in Rn=[0,An]d as a subset of Rd. We employ a stochastic sampling scheme that may create irregularly spaced sampling sites in a flexible manner and includes both pure and mixed increasing domain frameworks. We specifically examine the rate of the strong uniform convergence and the weak convergence of conditional U-processes when the explicative variable is functional. We examine the weak convergence where the class of functions is either bounded or unbounded and satisfies specific moment conditions. These results are achieved under somewhat general structural conditions pertaining to the classes of functions and the underlying models. The theoretical results developed in this paper are (or will be) essential building blocks for several future breakthroughs in functional data analysis.

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Kernel spatial density estimation in infinite dimension space

Cited by 16 publications

References 40 publications

Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

Nonparametric density estimation for intentionally corrupted functional data

Non-Parametric Conditional U-Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design

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