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HUUHTANEN, PENTTI:
Stochastic Complexity and the MDL Principle in Density Function
Estimation Academic Dissertation
June, 1998
This thesis has two main themes, density function estimation by
traditional, mainly nonparametric, methods with their consistency properties, and density
function estimation based on data dependent histogram estimators where smoothing is done
by the minimum description length principle. These two topics are tied together by the
information theoretic principles.
In the first part, we give a review of the traditional density function
estimation methods and the distance measures for the goodness of fit. Also more recent
methods in estimation are given, e.g. wavelet and neural network approaches.
In Chapter 4, we have given a thorough introduction to the stochastic
complexity and the minimum description length principle in the model selection. These
resulting criteria are based on information and coding theory and they offer totally new
ways for statistical inference. In Chapter 5 we have presented different new types of
density function estimation using this principle. The main theorem presented concerns the
asymptotic properties of the MDL type smoothing of the histogram density function
estimators, where we have shown that the MDL estimate of the number of bins satisfies the assumptions of
Lugosi–Nobel theorem which insure the a.s. convergence of the MDL estimators to the
true density. |
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NUMMI, TAPIO:
Estimation and Prediction in Growth Curve Models and Applications
Academic Dissertation
January, 1995
The main part of this thesis consists of six papers dealing with
estimation and prediction in growth curve models. The techniques used here are based on
the method of maximum likelihood (ML). As a computational method we use the iterative EM
(Expectation and Maximization) algorithm, which is easily implemented also in the presence
of incomplete or unbalanced data.
Estimation and prediction are considered under various types of model
for growth curves in this thesis. The growth curve model of Potthoff and Roy (1964) was
the starting-point, but the mixed effects models for repeated measurements are also
considered. Also the use of nonlinear models is discussed. Special emphasis is laid on
modelling the within-individual covariance structure parsimoniously.
We develop a prediction technique based on the iterative EM algorithm.
This technique is applied to a number of data sets with special attention to engineering
applications. The main focus was on the prediction of stem curve measurements for a
computerized forest harvester and on the prediction of quality variables of paper.
Estimation is considered in detail in the growth curve model of Potthoff and Roy with
random effects, assuming independent random errors. These results are extended to
estimation under parsimonious dependence structures within random errors and to estimation
under a multivariate random effects growth curve model. Estimation under incomplete data
and estimation of random effects are discussed. Also model selection problems arising in
the analysis of growth curves are considered. |
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SAARIO, VESA:
Some Techniques and Limiting Properties of the House-selling Problem
Academic Dissertation
April, 1994
The six papers contained in this thesis deal with a class of sequential
stochastic allocation problems, often referred to in the literature as the house-selling
problem, and the approach adopted in these papers is both theoretical and practical.
The theoretical part of this thesis contains derivations of the optimal
decision strategies which maximize the total expected payoff of the process, their
recurrence equations, and their limiting behaviour with some examples based on certain
well-known distribution families.
The suitability of the models to real-world financial decision-making
problems is discussed and the original house-selling problem is slightly modified to match
better these settings, such as by discounting future offers. Also, some house-selling
problems with structural extensions have been considered, and the Bayesian estimation
method is applied in determining the transition probabilities when sampling from the
Markov process. |
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THESES FOR MASTER OF SCIENCE
1994–1998
HUHTALA, HEINI:
Rintasyöpäseulonta (Screening for Breast Cancer)
Master's Thesis August 1995
HÄMÄLÄINEN, PETRI:
Kyselytutkimuksen tekeminen ja analysointi (Survey Design and
Analysis)
Master's Thesis August 1998
KAIPAINEN, HEIKKI:
Graafisia analyysimenetelmiä (Graphical Methods for Data Analysis)
Master's Thesis June 1995
KARVANEN, JUHA:
Stokastiset pisteprosessit ja niiden soveltaminen talouselämässä
(Stochastic Point Processes and Their Applications in Economics), Masters Thesis
December 1998
KORTE, HELI:
Tilastotiede tietoverkoissa
(Statistics in Information Networks)
Master's Thesis December 1997
LAINE, MARJO:
Virhekomponenttimallin soveltaminen paneeliaineistojen analyysiin
(Application of the Error Components Analysis to the Analysis of Panel Data)
Master's Thesis August 1997
LAMPELA, HEIKKI:
Teräksen mekaanisten ominaisuuksien hajonnan ja mittaustulosten
luotettavuuden tutkiminen tilastollisin menetelmin (Researching the Dispersion of the
Mechanical Properties of Steel and the Credibility of the Measurement Results Using
Statistical Methods)
Master's Thesis May 1995
MANNILA, LEENA:
Siirtofunktion ja kohinamallin mallinvalinta (Identification of
Tranfer Function Noise Models)
Master's Thesis May 1994
MÄENPÄÄ, JOUKO: Urheiluvedonlyönnin
kerroinanalyysi tilastollisin menetelmin (Coefficient Analysis for Sports Betting
by Statistical Methods)
Master's Thesis April 1997
MÄKELÄ, ERKKI:
Neurolaskenta ja sen tilastotieteellisiä sovellutuksia (Neural
Computing and its Statistical Applications)
Master's Thesis April 1998
SARKKI, SIRKKA:
Bootstrap (Bootstrap)
Master's Thesis October 1996
TOUKOMAA, HENRI:
Simulaation tehostaminen, esimerkkinä
Blackjack-korttipeli (Intensifying Simulation, Using Blackjack Card Game as an Example)
Master's Thesis April 1997
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