scholarly journals Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data

2013 ◽  
Vol 7 (0) ◽  
pp. 562-596 ◽  
Author(s):  
Hervé Cardot ◽  
Camelia Goga ◽  
Pauline Lardin
Keyword(s):  
Uniform Convergence ◽  
Functional Data ◽  
Confidence Bands ◽  
The Mean

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Consistency rates and asymptotic normality of the high risk conditional for functional data

2015 ◽  
Vol 7 (2) ◽  
pp. 220-242
Author(s):  
Abbes Rabhi ◽  
Latifa Keddani ◽  
Yassine Hammou
Keyword(s):  
High Risk ◽  
Asymptotic Normality ◽  
Uniform Convergence ◽  
Functional Data ◽  
Hazard Function ◽  
Convergence Properties ◽  
First Derivative ◽  
Nonparametric Estimates

AbstractThe maximum of the conditional hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates of the first derivative of the conditional hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum in the context of independence data.

scholarly journals Resampling methods for functional data

2018 ◽  
Author(s):  
Timothy McMurry ◽  
Dimitris Politis
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Nonparametric Regression ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Confidence Bands ◽  
Resampling Methods ◽  
Current State ◽  
Inference Techniques

This article examines the current state of methodological and practical developments for resampling inference techniques in functional data analysis, paying special attention to situations where either the data and/or the parameters being estimated take values in a space of functions. It first provides the basic background and notation before discussing bootstrap results from nonparametric smoothing, taking into account confidence bands in density estimation as well as confidence bands in nonparametric regression and autoregression. It then considers the major results in subsampling and what is known about bootstraps, along with a few recent real-data applications of bootstrapping with functional data. Finally, it highlights possible directions for further research and exploration.

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