159 research outputs found
Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests
Computerized adaptive testing is becoming increasingly popular due to
advancement of modern computer technology. It differs from the conventional
standardized testing in that the selection of test items is tailored to
individual examinee's ability level. Arising from this selection strategy is a
nonlinear sequential design problem. We study, in this paper, the sequential
design problem in the context of the logistic item response theory models. We
show that the adaptive design obtained by maximizing the item information leads
to a consistent and asymptotically normal ability estimator in the case of the
Rasch model. Modifications to the maximum information approach are proposed for
the two- and three-parameter logistic models. Similar asymptotic properties are
established for the modified designs and the resulting estimator. Examples are
also given in the case of the two-parameter logistic model to show that without
such modifications, the maximum likelihood estimator of the ability parameter
may not be consistent.Comment: Published in at http://dx.doi.org/10.1214/08-AOS614 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Conversation with Yuan Shih Chow
Yuan Shih Chow was born in Hubei province in China, on September 1, 1924. The
eldest child of a local militia and political leader, he grew up in war and
turmoil. His hometown was on the front line during most of the Japanese
invasion and occupation of China. When he was 16, Y. S. Chow journeyed, mostly
on foot, to Chongqing (Chung-King), the wartime Chinese capital, to finish his
high school education. When the Communist party gained power in China, Y. S.
Chow had already followed his university job to Taiwan. In Taiwan, he taught
mathematics as an assistant at National Taiwan University until he came to the
United States in 1954. At the University of Illinois, he studied under J. L.
Doob and received his Ph.D. in 1958. He served as a staff mathematician and
adjunct faculty at the IBM Watson Research Laboratory and Columbia University
from 1959 to 1962. He was a member of the Statistics Department at Purdue
University from 1962 to 1968. From 1968 until his retirement in 1993, Y. S.
Chow served as Professor of Mathematical Statistics at Columbia University. At
different times, he was a visiting professor at the University of California at
Berkeley, University of Heidelberg (Germany) and the National Central
University, Taiwan. He served as Director of the Institute of Mathematics of
Academia Sinica, Taiwan, and Director of the Center of Applied Statistics at
Nankai University, Tianjin, China. He was instrumental in establishing the
Institute of Statistics of Academia Sinica in Taiwan. He is currently Professor
Emeritus at Columbia University. Y. S. Chow is a fellow of the Institute of
Mathematical Statistics, a member of the International Statistical Institute
and a member of Taiwan's Academia Sinica. He has numerous publications,
including Great Expectations: The Theory of Optimal Stopping (1971), in
collaboration with Herbert Robbins and David Siegmund, and Probability Theory
(1978), in collaboration with Henry Teicher. Y. S. Chow has a strong interest
in mathematics education. He taught high school mathematics for one year in
1947 and wrote a book on high school algebra in collaboration with J. H. Teng
and M. L. Chu. In 1992, Y. S. Chow, together with I. S. Chang and W. C. Ho,
established the Chinese Institute of Probability and Statistics in Taiwan. This
conversation took place in the fall of 2003 in Dobbs Ferry, New York.Comment: Published at http://dx.doi.org/10.1214/088342304000000224 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Event History Analysis of Dynamic Communication Networks
Statistical analysis on networks has received growing attention due to demand
from various emerging applications. In dynamic networks, one of the key
interests is to model the event history of time-stamped interactions amongst
nodes. We propose to model dynamic directed communication networks via
multivariate counting processes. A pseudo partial likelihood approach is
exploited to capture the network dependence structure. Asymptotic results of
the resulting estimation are established. Numerical results are performed to
demonstrate effectiveness of our proposal
Likelihood Adaptively Modified Penalties
A new family of penalty functions, adaptive to likelihood, is introduced for
model selection in general regression models. It arises naturally through
assuming certain types of prior distribution on the regression parameters. To
study stability properties of the penalized maximum likelihood estimator, two
types of asymptotic stability are defined. Theoretical properties, including
the parameter estimation consistency, model selection consistency, and
asymptotic stability, are established under suitable regularity conditions. An
efficient coordinate-descent algorithm is proposed. Simulation results and real
data analysis show that the proposed method has competitive performance in
comparison with existing ones.Comment: 42 pages, 4 figure
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