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UID:8568@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250310T140000
DTEND;TZID=Europe/Paris:20250310T160000
DTSTAMP:20250124T125014Z
URL:https://www.i2m.univ-amu.fr/evenements/seminary-of-majewski-bartosz/
SUMMARY:Majewski Bartosz (AGH University of Krakow): Seminary of Majewski B
 artosz : Statistical inference for harmonizable processes
DESCRIPTION:Majewski Bartosz: An important class of processes used to model
  nonstationary signals is a class of harmonizable processes. These process
 es can be seen as the superposition of sine and cosine waves with random a
 mplitudes. Their analysis allows us to study how different signal frequenc
 ies are correlated with each other. Covariance between frequencies is most
 ly measured by the spectral density function\, while correlation is measur
 ed by the spectral coherence function.\n\nIn this talk\, we focus on harmo
 nizable processes whose spectral measure is concentrated on a union of lin
 es\, potentially with non-unit slopes. This class of processes is a genera
 lization of well-known\, almost periodically correlated processes. The pro
 cesses studied have practical applications in communication\, such as the 
 location of moving sources such as aircrafts\, rockets\, or hostile jammin
 g emitters that transmit signals.\n\nFirst\, we address the spectral densi
 ty estimation problem. We propose a periodogram frequency-smoothed along t
 he support line as the estimator. We establish the mean-square consistency
  of its normalized version\, considering scenarios where the support line 
 is known or unknown. In addition\, we derive the asymptotic distribution o
 f this estimator when the support line is known. Consequently\, we obtain 
 the asymptotic distribution of the spectral coherence estimator based on a
  periodogram frequency-smoothed along the support line. Moreover\, we intr
 oduce a consistent subsampling technique designed specifically for the spe
 ctral analysis of the considered class of processes. This technique enable
 s the construction of subsampling-based confidence intervals for spectral 
 characteristics. To validate the theoretical findings\, we provide a numer
 ical example applied to models commonly used in acoustics and communicatio
 n systems.\n\n[1] Dudek\, A.E.\, Majewski\, B. and Napolitano\, A. (2024)\
 , Spectral Density Estimation for a Class of Spectrally Correlated Process
 es. J. Time Ser. Anal.\, 45: 884-909. doi: 10.1111/jtsa.12742\n[2] Dudek A
 .E. and Majewski B. (2024)\, Asymptotic distribution and subsampling in sp
 ectral analysis for spectrally correlated processes. submitted on August 2
 024. preprint: https://hal.science/hal-04675084
CATEGORIES:Séminaire,Statistique
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
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