 STATISTICS SEMINAR
 Location: Room V104, Mathematics Building (Callaghan Campus) The University of Newcastle
 Dates: Thu, 28^{th} Feb 2013  Thu, 28^{th} Feb 2013
 Speaker: Sidra Safar, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Noniterative estimation methods for ordinal loglinear models
 Abstract for Noniterative estimation methods for ordinal loglinear models:
The loglinear models have been a significant area of research in the field of categorical
data analysis since the 1950s. However, until the mid1970s, loglinear models only
considered the modelling of nominal variables and did not make any assumption about
the ordering of categories of an ordinal variable. Therefore, the loglinear models have
been modified to incorporate the structure of any ordinal variable. This issue is
especially relevant in most fields of social science. The ordinal loglinear models are
amid the most widely used and powerful techniques to model association among the
ordinal variables in categorical data analysis. Traditionally, the parameters from such
models are estimated using iterative algorithms (such as the NewtonRaphson method,
and iterative proportional fitting), but issues such as choice of poor initial values and
contingency tables of larger dimensions can reduce the convergence rate as well as
highly increase the number of iterations required for the algorithms to converge.
More recent advances have suggested a method of noniterative estimation that gives
numerically similar estimates as that of the iterative methods for the estimation of linear
bylinear association parameter in an ordinal loglinear model for a twoway table. This
presentation will highlight the iterative and noniterative techniques commonly used to
estimate the linearbylinear association parameter from twodimensional ordinal log
linear models. It will provide an overview of how the growing number of noniterative
estimation techniques fit into the problem. Several possibilities to extend the research on
the noniterative estimates in order to validate their further use are discussed. The
presentation will also highlight the research undertaken so far to achieve this objective.
This includes considering the two fundamental estimates for the analysis of the
association between two categorical variables forming a contingency table and to
determine their asymptotic characteristics. A computational study is carried out for
contingency tables of varying sizes to show that these two estimates are asymptotically
unbiased. It is also shown that both estimates are asymptotically normally distributed.
On the basis of the standard errors, their relative efficiency has been established for 13
commonly analysed contingency tables that appear throughout the literature.
Keywords: Ordinal loglinear models, noniterative estimation, linearbylinear
association parameter, orthogonal polynomials, Newton Raphson, Iterative proportional
fitting.
 Speaker: Dr Glen Livingstone, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Fully Bayesian analysis of regime switching volatility models
 Abstract for Fully Bayesian analysis of regime switching volatility models:
The main aim of this thesis is to develop an automatic MCMC estimation
procedure for STARGARCH models that can be applied to any data set that
could normally be modeled by any of the subclasses of models that the
STARGARCH model generalises. This will remove the need for linearity
testing and model specification. The project will achieve three specific
objectives:
(i) to formulate a fully Bayesian analysis of univariate STAR models,
followed by univariate and multivariate STARGARCH models respectively;
(ii) to perform posterior analysis obtained in (i) by creating an
efficient MCMC algorithm and using simulation studies, implemented by
novel computer code in R;
(iii) to apply the MCMC estimation algorithm to real world data to
examine regimeswitching and varying volatility in the data.
 Abstract for Noniterative estimation methods for ordinal loglinear models:
The loglinear models have been a significant area of research in the field of categorical
data analysis since the 1950s. However, until the mid1970s, loglinear models only
considered the modelling of nominal variables and did not make any assumption about
the ordering of categories of an ordinal variable. Therefore, the loglinear models have
been modified to incorporate the structure of any ordinal variable. This issue is
especially relevant in most fields of social science. The ordinal loglinear models are
amid the most widely used and powerful techniques to model association among the
ordinal variables in categorical data analysis. Traditionally, the parameters from such
models are estimated using iterative algorithms (such as the NewtonRaphson method,
and iterative proportional fitting), but issues such as choice of poor initial values and
contingency tables of larger dimensions can reduce the convergence rate as well as
highly increase the number of iterations required for the algorithms to converge.
More recent advances have suggested a method of noniterative estimation that gives
numerically similar estimates as that of the iterative methods for the estimation of linear
bylinear association parameter in an ordinal loglinear model for a twoway table. This
presentation will highlight the iterative and noniterative techniques commonly used to
estimate the linearbylinear association parameter from twodimensional ordinal log
linear models. It will provide an overview of how the growing number of noniterative
estimation techniques fit into the problem. Several possibilities to extend the research on
the noniterative estimates in order to validate their further use are discussed. The
presentation will also highlight the research undertaken so far to achieve this objective.
This includes considering the two fundamental estimates for the analysis of the
association between two categorical variables forming a contingency table and to
determine their asymptotic characteristics. A computational study is carried out for
contingency tables of varying sizes to show that these two estimates are asymptotically
unbiased. It is also shown that both estimates are asymptotically normally distributed.
On the basis of the standard errors, their relative efficiency has been established for 13
commonly analysed contingency tables that appear throughout the literature.
Keywords: Ordinal loglinear models, noniterative estimation, linearbylinear
association parameter, orthogonal polynomials, Newton Raphson, Iterative proportional
fitting.
 Abstract for Fully Bayesian analysis of regime switching volatility models:
The main aim of this thesis is to develop an automatic MCMC estimation
procedure for STARGARCH models that can be applied to any data set that
could normally be modeled by any of the subclasses of models that the
STARGARCH model generalises. This will remove the need for linearity
testing and model specification. The project will achieve three specific
objectives:
(i) to formulate a fully Bayesian analysis of univariate STAR models,
followed by univariate and multivariate STARGARCH models respectively;
(ii) to perform posterior analysis obtained in (i) by creating an
efficient MCMC algorithm and using simulation studies, implemented by
novel computer code in R;
(iii) to apply the MCMC estimation algorithm to real world data to
examine regimeswitching and varying volatility in the data.
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