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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.

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.