 A Non‐Parametric Estimator of the Spectral Density of a Continuous‐Time Gaussian Process Observed at Random TimesJean‐marc Bardet and Pierre R. Bertrand Scandinavian Journal of Statistics, 2010, vol. 37, issue 3, 458-476 Abstract: Abstract. In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a non‐parametric estimator of the spectral density of a Gaussian process with stationary increments (or a stationary Gaussian process) from the observation of one path at random discrete times. For every positive frequency, this estimator is proved to satisfy a central limit theorem with a convergence rate depending on the roughness of the process and the moment of random durations between successive observations. In the case of stationary Gaussian processes, one can compare this estimator with estimators based on the empirical periodogram. Both estimators reach the same optimal rate of convergence, but the estimator based on wavelet analysis converges for a different class of random times. Simulation examples and an application to biological data are also provided. Date: 2010 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:37:y:2010:i:3:p:458-476 Ordering information: This journal article can be ordered from Access Statistics for this article Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association |
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