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Is the Brownian bridge a good noise model on the boundary of a circle?
- Source :
- Annals of the Institute of Statistical Mathematics. 69:389-416
- Publication Year :
- 2015
- Publisher :
- Springer Science and Business Media LLC, 2015.
-
Abstract
- In this paper we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together with their expansion in random Fourier series in order to provide results about their path regularity. Finally, we discuss a simple and flexible parametric model with prescribed regularity that is used in applications, and we prove the asymptotic properties of the maximum likelihood estimates of model parameters.<br />24pp, final version; the final publication is available at http://www.ism.ac.jp/editsec/aism/
- Subjects :
- Statistics and Probability
Stochastic process
Probability (math.PR)
010102 general mathematics
Boundary (topology)
Mathematics - Statistics Theory
Statistics Theory (math.ST)
Brownian bridge
01 natural sciences
Primary 42A16, Secondary 60B15, 60G15
010104 statistics & probability
Noise
symbols.namesake
Fourier transform
Parametric model
FOS: Mathematics
symbols
Applied mathematics
0101 mathematics
Fourier series
Gaussian process
Mathematics - Probability
Mathematics
Subjects
Details
- ISSN :
- 15729052 and 00203157
- Volume :
- 69
- Database :
- OpenAIRE
- Journal :
- Annals of the Institute of Statistical Mathematics
- Accession number :
- edsair.doi.dedup.....713935bb9cf3054d2ca3afcdefd07f4f