Law of large numbers for discretely observed random functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10365484" target="_blank" >RIV/00216208:11320/17:10365484 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S1226319217300261" target="_blank" >http://www.sciencedirect.com/science/article/pii/S1226319217300261</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jkss.2017.04.002" target="_blank" >10.1016/j.jkss.2017.04.002</a>

Result language
angličtina
Original language name
Law of large numbers for discretely observed random functions
Original language description
A strong law of large numbers for continuous random functions, and associated tensor product surfaces is established in the setup of discretely observed functional data. The result is shown in the framework of uniform convergence of functions, and stated without imposing any distributional assumptions. It is demonstrated that, under mild conditions, laws of large numbers for continuously observed functional data imply the corresponding laws under the discrete observational design of functions. Applications to the problem of estimation of expectation functions and covariance surfaces for discretely observed functional data are discussed.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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