Research

The main research areas within the Statistics group are linear models, multivariate analysis, time series analysis, asymptotic methods in Statistics, computers in statistical training, 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 analytical research the main emphasis is 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.