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UID:0-449@aerospace.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20170215T163000

DTEND;TZID=Asia/Jerusalem:20170215T173000

DTSTAMP:20230603T190334Z

URL:https://aerospace.technion.ac.il/events/crlb-for-likelihood-functions-
 with-parameter-dependent-support-and-a-new-bound/

SUMMARY:CRLB for Likelihood Functions with Parameter-Dependent Support and 
 a New Bound
DESCRIPTION:Lecturer:Yaakov Bar-Shalom\n Faculty:\n Institute:University of
  Connecticut\n Location:Classroom 165\, ground floor\, Library\, Aerospace
  Eng.\n Zoom: \n Abstract: \n Details: \n In this talk we discuss the regu
 larity conditions required for the classical Cram´er-Rao lower bound (CR
 LB) for real-valued (nonrandom unknown) parameters to hold. It is shown t
 hat the commonly assumed requirement that the support of the likelihood 
 function (LF) should be independent of the parameter to be estimated can 
 be replaced by the much weaker requirement that the LF is continuous at t
 he end points of its support.\nParameter-dependent support of the LF arise
 s when an unknown parameter is observed in the presence of additive measu
 rement noise and the measurement noise probability density function (pdf)
  has a finite support. It is also pointed out that the commonly cited re
 quirements of absolute integrability of the first two derivatives of the L
 F should be replaced by requirements on the log-LF (LLF). Some practical
  examples of finite-support measurement noises\, which lead to parameter-
 dependent LF support\, are discussed in light of the above. For the case 
 where the LF is not continuous at the end points of its support\, a new m
 odified CRLB — designated as the Cram´er-Rao-Leibniz lower bound (CRLL
 B)\, since it relies on Leibniz integral rule — is presented and its us
 e illustrated. The CRLLB is shown to provide valid bounds for a number of
  long-standing problems for which the CRLB was shown in the literature a
 s not valid\, in particular\, for a uniformly distributed measurement noi
 se.
CATEGORIES:Seminars
LOCATION:Classroom 165\, ground floor\, Library\, Aerospace Eng.

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