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1 
Testing dispersion parameters in generalized linear models.January 1990 (has links)
by Lam Man Kin. / Thesis (M.Phil.)Chinese University of Hong Kong, 1990. / Bibliography: leaves 6971. / Chapter Chapter 1  Introduction  p.1 / Chapter Chapter 2  Generalized Linear Models  p.7 / Chapter §2.1  The Model  p.7 / Chapter §2.2  Estimation of the Parameters  p.10 / Chapter Chapter 3  Tests for the Dispersion Parameters  p.15 / Chapter S3.1  Three Asymptotically Equivalent Tests based on MLE  p.15 / Chapter §3.2  Application of the Tests for the Dispersion Parameters  p.22 / Chapter Chapter 4  Finite Sample Study of the Three Tests based on Simulation  p.29 / Chapter §4.1  Introduction  p.29 / Chapter §4.2  The Simulation  p.31 / Chapter §4.3  The Results  p.34 / Chapter Chapter 5  An Example  p.38 / Chapter Chapter 6  Conclusions and Discussions  p.42 / Tables / References

2 
The laplace approximation and inference in generalized linear models with two or more random effectsPratt, James L. 29 November 1994 (has links)
This thesis proposes an approximate maximum likelihood estimator and
likelihood ratio test for parameters in a generalized linear model when two or
more random effects are present. Substantial progress in parameter estimation
for such models has been made with methods involving generalized least squares
based on the approximate marginal mean and covariance matrix. However, tests
and confidence intervals based on this approach have been limited to what is
provided through asymptotic normality of estimates. The proposed solution is
based on maximizing a Laplace approximation to the loglikelihood function.
This approximation is remarkably accurate and has previously been
demonstrated to work well for obtaining likelihood based estimates and
inferences in generalized linear models with a single random effect. This thesis
concentrates on extensions to the case of several random effects and the
comparison of the likelihood ratio inference from this approximate likelihood
analysis to the Waldlike inferences for existing estimators.
The shapes of the Laplace approximate and true loglikelihood functions
are practically identical, implying that maximum likelihood estimates and
likelihood ratio inferences are obtained from the Laplace approximation to the
loglikelihood. Use of the Laplace approximation circumvents the need for
numerical integration, which can be practically impossible to compute when
there are two random effects. However, both the Laplace and exact (via
numerical integration) methods require numerical optimization, a sometimes
slow process, for obtaining estimates and inferences.
The proposed Laplace method for estimation and inference is
demonstrated for three real (and some simulated) data sets, along with results
from alternative methods which involve use of marginal means and covariances.
The Laplace approximate method and another denoted as Restricted Maximum
Likelihood (REML) performed rather similarly for estimation and hypothesis
testing. The REML approach produced faster analyses and was much easier to
implement while the Laplace implementation provided likelihood ratio based
inferences rather than those relying on asymptotic normality. / Graduation date: 1995

3 
Likelihoodbased inference for tweedie generalized linear models /Dunn, Peter Kenneth. January 2001 (has links) (PDF)
Thesis (Ph. D.)University of Queensland, 2001. / Includes bibliographical references.

4 
Discrepancybased model selection criteria using cross validation /Davies, Simon January 2002 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 155159). Also available on the Internet.

5 
Discrepancybased model selection criteria using cross validationDavies, Simon January 2002 (has links)
Thesis (Ph. D.)University of MissouriColumbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 155159). Also available on the Internet.

6 
On some extensions of generalized linear models with varying dispersionWu, Kayui, Karl., 胡家銳. January 2012 (has links)
When dealing with exponential family distributions, a constant dispersion
is often assumed since it simplifies both model formulation and estimation.
In contrast, heteroscedasticity is a common feature of almost every empirical
data set. In this dissertation, the dispersion parameter is no longer considered
as constant throughout the entire sample, but defined as the expected
deviance of the individual response yi and its expected value _i such that it
will be expressed as a linear combination of some covariates and their coefficients.
At the same time, the dispersion regression is an essential part of a
double Generalized Linear Model in which mean and dispersion are modelled in two interlinked and pseudosimultaneously estimated submodels.
In other words, the deviance is a function of the response mean which on the
other hand depends on the dispersion. Due to the mutual dependency, the
estimation algorithm will be iterated as long as the improvement of the one
parameter leads to significant changes of the other until it is not the case.
If appropriate covariates are chosen, the model’s goodness of fit should
be improved by the property that the dispersion is estimated by external
information instead of being a constant. In the following, the advantage
of dispersion modelling will be shown by its application on three different
types of data: a) zeroinflated data, b) nonlinear time series data, and
c) clinical trials data. All these data follow distributions of the exponential
family for which the application of the Generalized Linear Model is justified,
but require certain extensions of modelling methodologies.
In this dissertation, The enhanced goodness of fit given that the constant
dispersion assumption is dropped will be shown in the above listed
examples. In fact, by formulating and carrying out score and Wald tests
on testing for the possible occurrence of varying dispersion, evidence of
heterogeneous dispersion could be found to be present in the data sets considered.
Furthermore, although model formulation, asymptotic properties
and computational effort are more extensive when dealing with the double
models, the benefits and advantages in terms of improved fitting results and
more efficient parameter estimates appear to justify the additional effort not
only for the types of data introduced, but also generally for empirical data
analysis, on different types of data as well. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

7 
Linear model diagnostics and measurement error07 September 2010 (has links)
The general linear model, the weighted linear model, and the generalized linear model are presented in detail. Diagnostic tools for the linear models are considered. In general the standard analysis for linear models does not account for measurement error. / Thesis (M.Sc.)  University of KwaZuluNatal, Pietermaritzburg, 2007.

8 
Estimation and selection in additive and generalized linear modelsFeng, Zhenghui 01 January 2012 (has links)
No description available.

9 
Model identification and parameter estimation of stochastic linear models.Vazirinejad, Shamsedin. January 1990 (has links)
It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errorsinvariables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errorsinvariables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multiequation model similar to the simultaneousequations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multiequation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.

10 
Ftests in partially balanced and unbalanced mixed linear modelsUtlaut, Theresa L. 11 February 1999 (has links)
This dissertation considers two approaches for testing hypotheses in
unbalanced mixed linear models. The first approach is to construct a design with
some type of structure or "partial" balance, so that some of the optimal properties of
a completely balanced design hold. It is shown that for a particular type of partially
balanced design certain hypothesis tests are optimal. The second approach is to
study how the unbalancedness of a design affects a hypothesis test in terms of level
and power. Measures of imbalance are introduced and simulation results are
presented that demonstrate the relationship of the level and power of a test and the
measures.
The first part of this thesis focuses on error orthogonal designs which are a
type of partially balanced design. It is shown that with an error orthogonal design
and under certain additional conditions, ANOVA Ftests about certain linear
combinations of the variance components and certain linear combinations of the
fixed effects are uniformly most powerful (UMP) similar and UMP unbiased. The
ANOVA Ftests for the variance components are also invariant, so that the tests are
also UMP invariant similar and UMP invariant unbiased. For certain simultaneous
hypotheses about linear combinations of the fixed effects, the ANOVA Ftests are
UMP invariant unbiased.
The second part of this thesis considers a mixed model with a random
nested effect, and studies the effects of an unbalanced design on the level and
power of a hypothesis test of the nested variance component being equal to zero.
Measures of imbalance are introduced for each of the four conditions necessary to
obtain an exact test. Simulations are done for two different models to determine if
there is a relationship between any of the measures and the level and power for both
a naive test and a test using Satterthwaite's approximation. It is found that a
measure based on the coefficients of the expected mean squares is indicative of
how a test is performing. This measure is also simple to compute, so that it can
easily be employed to determine the validity of the expected level and power. / Graduation date: 1999

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