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DTSTART:19700927T020000
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CATEGORIES:SMS Seminars
CONTACT: Estate Khmaladze\, Professor Emeritus
DESCRIPTION:\n\n[Due to the unforeseen circumstances\, the seminar had to b
 e moved. Thanks for your patience.]\n\n\n\n\n\nThe talk represents part of
  the material from the speaker's joint work with Sara Algeri (U.Minnesota)
 . The talk could have been called ``Statistical analysis of large number o
 f infrequent events"\, or ``On theory of Poisson regression"\, or ``When P
 earson's chi^2 is not a goodness of fit test". Whatever it is called\, it 
 is clear we will start with well trodden topic of statistics - and if we t
 hink\, as the speaker did\, that we have enough knowledge about the phenom
 ena there\, or enough intuition about the subject\, we may be not entirely
  correct.\n\nThe talk is our attempt to say something useful for everyday 
 statistical work. The key words are:\n\ndivisible statistics\, fine partit
 ioning\, large number of groups (or urns\, boxes\, pixels\, etc.)\, contig
 uous alternatives\, useless parts of useful tests\, real astronomical data
 \, testing uniformity\, spectral statistics\, statistics of empty boxes.\n
 \nSara Algeri\, Estate V. Khmaladze (2026)\, On the statistical analysis o
 f grouped data: when Pearson chi^2 and other divisible statistics are not 
 goodness-of-fit\, JRSS B\, September 26\, online - 23 June 2026.\n\n===An 
 updated/extended abstract:======\n\nThe previous abstract is valid - but 1
  hour is not enough.\n\nSo\, I would much rather say and illustrate one th
 ing\, but clearly - good enough for p/g students\, than to cover large par
 t of S.Algeri-Khm in more telegraphic manner.\n\nTherefore\, out of five t
 opics below let me\, please\, describe and illustrate mostly B. -- but wit
 h better clarity.\n\nHow to create a unified approach to the theory: not \
 \chi^2 separately and spectral statistics separately\, as "similar but dif
 ferent"\, but as the same object - linear functional from a single empiric
 al process.\nWhy for any given divisible statistic we can construct anothe
 r divisible statistic with uniformly better power against all contiguous a
 lternatives. For example\, why one can construct a test\, uniformly better
  than K.Pearson's \\chi^2?\nWhen the hypothesis is parametric\, one will n
 eed to estimate the parameter. However\, frequently expressed "We'd like t
 o know exact value\, but unfortunately..." is incorrect attitude\, because
  estimation of parameter gives an advantage in power.\nWhen we need to est
 imate parameter\, based on divisible statistic\, do we know what is the be
 st estimating equation? - We do\, which is a Cram\\'er-Rao type result.\nO
 ne cannot have a goodness of fit(GoF) test based on one or "few" divisible
  statistics. But can we have a GoF test based on partial sums' process? --
  Yes\, we can construct a class of such processes\, and they will lead to 
 GoF tests with analytically known limit distributions.
DTEND;TZID=Pacific/Auckland:20260807T150000
DTSTAMP:20260803T233921Z
DTSTART;TZID=Pacific/Auckland:20260807T140000
LOCATION:Cotton Club\, Cotton 350
ORGANIZER: Estate Khmaladze\, Professor Emeritus
SUMMARY: Estate Khmaladze\, Professor Emeritus - [SMS seminar] On statistic
 al analysis of grouped data
UID:seminar_sms1038_20260728110131
URL:
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