Head: |
Nicholay A. Nechval, Dr.Hab.Sc.Ing., Professor |

Members: |
Konstantin N. Nechval, M.Sc. |

**Topics of Research and Main Results**

The present research has been devoted to the further development and perfection of methods of statistical analysis and efficient decision making on small samples of the data. This problem remains today perhaps the most difficult and important of all the problems of mathematical statistics that require considerable efforts and great skill for investigation. The greater part of results obtained in mathematical statistics have nice asymptotic properties, i. e., ones are efficient on large samples of the data. However, in practice, we deal, as a rule, with small samples.

It is assumed that the following problems will be considered on small samples of the data:

Goodness-of-fit testing and hypothesis testing for truncated distributions.

Goodness-of-fit testing and hypothesis testing on censored samples of the data.

Detection, recognition, classification and adaptive control under conditions of incompleteness of obtained information.

The fundamental approaches that will be used for investigations, are both the transformation of the observed data and the principle of invariance.

The results obtained will be used in such fields as digital signal and image processing, decision making in economics, diagnosis in medicine, control in ecology, etc.

This research has been supported in part by a research grant GR-96.0213 provided by the Latvian Council of Science and the National Institute of Mathematics and Informatics of Latvia.

**Selected Publications**

- Nechval, K.N. and Nechval, N.A. (1999). Constructing lower simultaneous prediction limits on observations in future samples from the past data. :COMPUTERS AND INDUSTRIAL ENGINEERING, Vol. 37, 1999, pp. 133-136.
- Nechval, N.A. and Nechval, K.N. (1999). Applications of invariance to estimation of safety stock levels in inventory model. COMPUTERS AND INDUSTRIAL ENGINEERING, Vol. 37, 1999, pp. 247-250.
- Nechval, N.A. and Nechval, K.N. (2000). Adaptive optimization in stochastic systems via fiducial approach. CASYS (International Journal of Computing Anticipatory Systems), Vol. 6, 2000, pp. 309-327.
- Nechval, N.A. and Nechval, K.N. (2000). Detecting a change point in a sequence of small area statistics. STATISTICS IN TRANSITION, Vol. 4, No. 4, March 2000, pp. 699-710.
- Nechval N.A., Nechval K.N., Heimanis B.M. (1998). Variational approach to adaptive optimization of stochastic systems. CYBERNETICS AND SYSTEMS в98, R. Trappl (ed.), Vol. 1, Vienna: AUSTRIAN SOCIETY FOR CYBERNETIC STUDIES, 1998, pp. 44-49..
- Nechval, N.A. and Nechval, K.N. (2000). State estimation of stochastic systems via invariant embedding technique. CYBERNETICS AND SYSTEMS'2000, R. Trappl (ed.), Vol. 1. Austrian Society for Cybernetic Studies, Vienna, 2000, pp. 96-101.
- Nechval, K.N. and Nechval, N.A. (2000). Adaptive control of airline booking levels. In: CYBERNETICS AND SYSTEMS'2000, R. Trappl (ed.), Vol. 2. Austrian Society for Cybernetic Studies, Vienna, 2000, pp. 507-512.