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The main research areas within the Statistics group are linear models, multivariate analysis, time series analysis, asymptotic methods in Statistics, computers in statistical training, expert systems and design of experiments.

One line of research in linear models has been biased estimation, which provides alternatives to the ordinary least squared estimator. For example, ridge regression and restricted least squares estimation, under linear stochastic and deterministic restrictions, fall into this category. Comparison of estimators with respect to a mean square error matrix has led to the study of matrix orderings, which is also of considerable importance in matrix theory. The effects of influential observations and the problems caused by multicollinearity have been studied in both regression analysis and multivariate growth curve analysis. Multivariate growth curve models have been studied both from the theoretical and computational point of view. Also empirical research has been done in this area.

The relative goodness of ordinary least squares (OLS) estimation with respect to the best linear unbiased (BLU) estimation in the general linear model has also been under study. A fruitful concept in this context appears to concern the canonical correlations between the ordinary least squares fitted values and the residuals. The relative goodness of the OLS estimator can be expressed as a function of these canonical correlations. Various properties of these canonical correlations are examined when the covariance matrix of the error vector is allowed to be singular and the model matrix may not have a full column rank. Also some features of the BLUE's covariance matrix can be characterized using these canonical correlations. Further, following a wider interpretation proposed by Rao (1971), weighted least squares estimators are considered and several properties of such estimators are discussed. These properties are then applied to derive a number of criteria for WLSE to coincide with BLUE.

Recently, studies have been made dealing with a general partitioned linear model and a corresponding specifically reduced model. Particular attention has beeen paid on conditions for the BLUE for the expectation of the observable random vector under the reduced model to remain BLUE in the partitioned model. Furthermore, alternative linear estimators and their coincidence with the BLUE under the partitioned model have been studied.

In time series research the main emphasis has been on the identification and estimation of both univariate and vector valued Box and Jenkins models. The identification and study of model selection criteria together with estimation (especially initial estimation) have comprised the most important research topics. Both time and frequency domain methods have been studied in this context. Modelling of nonlinear processes has been investigated by using neural networks.

The use of asymptotic methods in Statistics has mainly focused on the application of the so-called weak convergence of stochastic processes to time-varying parameter problems and to multivariate nonparametrics. The other main theme, closely connected with the former, is the use of the Pitman approach to asymptotic efficiency, especially in nonstandard cases.

The main goal of research in the area of the statistical expert systems is to design and implement experimental research vehicles for studying the use of artificial intelligence techniques (e.g. logic programming languages, knowledge bases, heuristic rules) in producing statistical expert systems. For example, in the implementation of a prototype expert system we have tried to make explicit statistical knowledge applied in the domain of preliminary time series analysis. Also, special attention has been paid to the user interface issues of statistical expert systems.

Modelling the behavior of repeated measurements, also called longitudinal data, has been the subject of research since the early 1980 within Statistics Unit. The Academy of Finland has funded the following research projects on the above mentioned topics and their applications:

Analysis of Longitudinal Data (1.8.1990–31.7.1993) headed by Esko Leskinen (University of Jyväskylä), Erkki Liski and Gunnar Rosenqvist (Swedish School of Economics).

Developing an Integrated System for Forest Harvesting (1993–1994) headed by Erkki Liski, funded by the Ministry of Education.

Analysis of Covariance Structures (1995–1996) headed by Erkki Liski and Götz Trenkler (University of Dortmund), funded jointly by the Academy of Finland and Deuche Akademische Austausch Dienst.

Developing of Forest Harvesting Systems by Utilizing Statistical Methods (1997–1999) headed by Erkki Liski.

The effective use of Statistical methods have become possible by the appearance of modern computer-controlled forest harvesters. There are four mutually supportive parts within this project:

1. Utilization of prior information and pre-harvest measurements

2. Modelling and prediction of tree stems and bucking in cases of incomplete information.

3. The log mix problem and selection of stands for felling

4. Sampling and experi-mental design

5. Forest harvesting simulator program

The focus of this research is on the application of statistical methods in the areas named above. The basis of the information system should be efficient and comprehensive data collection and data management, which offer an opportunity for the application of mathematical-statistical methods.

A relatively lightweight method is needed in order to estimate the quantity and structure of standing timber for planning the harvesting of forests. Sampling data or information obtained from comparable stumpage are used to update the prior information on the standing timber. The estimates based on the log distribution is the basis of planning forest harvesting according to desired criteria. A mixed model approach has proved repeated-measurements to be a flexible tool for stem curve modelling and prediction. The aim is to develop these methods more suitable for practical purposes.

Our group has studied optimal designs for estimation and prediction in linear random coefficient regression models and growth curve models. The results are applied to tree stem data collected by forest harvesters. We have also introduced and investigated so-called DS-optimality criterion.

The project’s homepage is: https://webpages.tuni.fi/uta_statistics/puuprojekti1997/.

Advanced Methods for Computer-Aided Bucking of Scots Pine, (2001-) headed by Tapio Nummi.