what is Marshall olkin transformation? When it is first used and why we need it? Simply explain background of this transformation?

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Read this and then explain what is Marshall olkin transformation? When it is first used and why we need it? Simply explain background of this transformation? I have only this two pictures of this may be it is relevant or not?
10:06
Answer 1 of 1
In the 1970s, Olkin turned his attention to
the problem of moment estimation in the
presence of multivariate data. He developed
the method of moments estimation, which
is a generalization of the method of
moments estimation for univariate data. He
also showed that the method of moments
estimation is asymptotically efficient in the
presence of multivariate data.
In the 1980s, Olkin developed the theory of
order statistics for multivariate data. He
showed that the distribution of the order
statistics of a multivariate random vector is
a generalization of the univariate case. He
also derived the asymptotic distribution of
the order statistics of a multivariate random
vector.
Olkin has also made contributions to the
fields of nonparametric statistics and time
series analysis. In the field of nonparametric
statistics, he has developed the theory of
rank-based nonparametric tests. In the field
of time series analysis, he has developed
the theory of autoregressive moving
Done
average processes.
Olkin has been a member of the National
Academy of Sciences since 1975. He is a
Fellow of the American Statistical
Association and the Institute of
Mathematical Statistics. He has also been a
Guggenheim Fellow and a Fulbright Scholar.
Olkin has received many honors and awards
for his contributions to statistics. In
particular, he has been awarded the
Dumnidantal Anal of the lotitia of
Transcribed Image Text:10:06 Answer 1 of 1 In the 1970s, Olkin turned his attention to the problem of moment estimation in the presence of multivariate data. He developed the method of moments estimation, which is a generalization of the method of moments estimation for univariate data. He also showed that the method of moments estimation is asymptotically efficient in the presence of multivariate data. In the 1980s, Olkin developed the theory of order statistics for multivariate data. He showed that the distribution of the order statistics of a multivariate random vector is a generalization of the univariate case. He also derived the asymptotic distribution of the order statistics of a multivariate random vector. Olkin has also made contributions to the fields of nonparametric statistics and time series analysis. In the field of nonparametric statistics, he has developed the theory of rank-based nonparametric tests. In the field of time series analysis, he has developed the theory of autoregressive moving Done average processes. Olkin has been a member of the National Academy of Sciences since 1975. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. He has also been a Guggenheim Fellow and a Fulbright Scholar. Olkin has received many honors and awards for his contributions to statistics. In particular, he has been awarded the Dumnidantal Anal of the lotitia of
Marshall Olkin is an American statistician
who has made significant contributions to
the fields of multivariate analysis and
distribution theory. He is best known for his
work on the multivariate normal distribution
and its generalizations, as well as for his
development of the method of moments
estimation.
Olkin was born in New York City in 1930. He
received his bachelor's degree in
mathematics from Brooklyn College in 1951,
and his master's and Ph.D. in statistics from
Stanford University in 1952 and 1955
respectively. After completing his Ph.D.,
Olkin joined the statistics faculty at the
University of California, Berkeley, where he
remained for his entire career.
Olkin's early work focused on the
multivariate normal distribution and its
generalizations. In particular, he derived the
moment estimators for the mean and
variance of the multivariate normal
distribution, and showed that these
estimators are asymptotically efficient. He
also developed the theory of elliptically
contoured distributions, which are
generalizations of the multivariate normal
distribution.
Transcribed Image Text:Marshall Olkin is an American statistician who has made significant contributions to the fields of multivariate analysis and distribution theory. He is best known for his work on the multivariate normal distribution and its generalizations, as well as for his development of the method of moments estimation. Olkin was born in New York City in 1930. He received his bachelor's degree in mathematics from Brooklyn College in 1951, and his master's and Ph.D. in statistics from Stanford University in 1952 and 1955 respectively. After completing his Ph.D., Olkin joined the statistics faculty at the University of California, Berkeley, where he remained for his entire career. Olkin's early work focused on the multivariate normal distribution and its generalizations. In particular, he derived the moment estimators for the mean and variance of the multivariate normal distribution, and showed that these estimators are asymptotically efficient. He also developed the theory of elliptically contoured distributions, which are generalizations of the multivariate normal distribution.
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