## Estymacja średniej w schematach rotacyjnych

### Jan Kowalski

#### Abstract

The framework of this paper is optimal mean estimation in repeated surveys, with predesigned scheme for rotation of elements in the sample. Our main objective is to find linear representation of the BLUE with respect to optimal estimators obtained on previous occasions. One advantage of such recursive form is considerably reduced cost of computing the BLUE. The most important result (obtained after imposing some restrictions on correlation structure and the rotation scheme) is a sufficient condition for existence of solution to the recurrence problem. Its verification involves analysis of roots of a certain polynomial with real coefficients. We provide also an effective algorithm for computing the desired recursive form of the BLUE and give examples of applications.Diploma type | Doctor of Philosophy | ||||

Author |
Jan Kowalski (FMIS)
Jan Kowalski
| ||||

Title in Polish | Estymacja średniej w schematach rotacyjnych | ||||

Language | pl polski | ||||

Certifying Unit | Faculty of Mathematics and Information Science (FMIS) | ||||

Discipline | mathematics / (mathematics domain) / (physical sciences) | ||||

Defense Date | 26-04-2010 | ||||

End date | 20-05-2010 | ||||

Supervisor |
Jacek Wesołowski (FMIS / DPMS)
Jacek Wesołowski
| ||||

Internal reviewers |
Paweł Szabłowski (FMIS / DAST)
Paweł Szabłowski
| ||||

External reviewers |
Wojciech Niemiro
Wojciech Niemiro
| ||||

Pages | 120 | ||||

Keywords in English | xxx | ||||

Abstract in English | The framework of this paper is optimal mean estimation in repeated surveys, with predesigned scheme for rotation of elements in the sample. Our main objective is to find linear representation of the BLUE with respect to optimal estimators obtained on previous occasions. One advantage of such recursive form is considerably reduced cost of computing the BLUE. The most important result (obtained after imposing some restrictions on correlation structure and the rotation scheme) is a sufficient condition for existence of solution to the recurrence problem. Its verification involves analysis of roots of a certain polynomial with real coefficients. We provide also an effective algorithm for computing the desired recursive form of the BLUE and give examples of applications. | ||||

Thesis file |
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Citation count* | 5 (2020-10-22) |

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