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Some investigations in minimax estimation theory

100%
Trybuła S.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction.............................................................................................................................................................................................5 2. A theorem for a multinomial population...................................................................................................................................................5 3. Estimation of frequencies of population with a hierarchic structure........................................................................................................7 4. Estimation of frequencies of multinomial population under a general quadratic loss Function..............................................................12 5. A problem of prediction.........................................................................................................................................................................15 6. Minimax estimation of distribution function............................................................................................................................................17 7. Sequential minimax estimation for stochastic processes in the case where there exists a sufficient statistic for the parameter............18 8. Sequential estimation for the multinomial process.................................................................................................................................21 9. Exponential family of processes............................................................................................................................................................23 10. Sequential estimation for a multivariate process.................................................................................................................................24 11. Sequential estimation for the Poisson process....................................................................................................................................29 12. Sequential minimax estimation in the case where the set of a priori distributions of the parameter is restricted.................................31 13. Continuation to Section 12..................................................................................................................................................................37 14. Final remarks......................................................................................................................................................................................40 References...............................................................................................................................................................................................41
2
Content available remote

A noisy duel under arbitrary motion. IX

95%
Trybuła S.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 3
261-277
3
Content available remote

Minimax mutual prediction

95%
Trybuła S.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 4
437-444
EN
The problems of minimax mutual prediction are considered for binomial and multinomial random variables and for sums of limited random variables with unknown distribution. For the loss function being a linear combination of quadratic losses minimax mutual predictors are determined where the parameters of predictors are obtained by numerical solution of some equations.
4
Content available remote

A noisy duel under arbitrary motion. VIII

95%
Trybuła S.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 2
135-149
5
Content available remote

A mixed duel under arbitrary motion and uncertain existence of the shot

95%
Trybuła S.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 1
39-44
EN
The purpose of the paper is to solve a mixed duel in which the numbers of shots given to the players are independent 0-1-valued random variables. The players know their distributions as well as the accuracy function P, the same for both players. It is assumed that the players can move as they like and that the maximal speed of the first player is greater than that of the second player. It is shown that the game has a value, and a pair of optimal strategies is found.
6
Content available remote

A noisy duel under arbitrary motion. VII

95%
Trybuła S.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 1
37-49
7
Content available remote

Minimax mutual prediction of multinomial random variables

95%
Trybuła S.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 4
371-377
EN
The problem of minimax mutual prediction is considered for multinomial random variables with the loss function being a linear combination of quadratic losses connected with prediction of particular variables. The basic parameter of the minimax mutual predictor is determined by numerical solution of some equation.
8
Content available remote

Simultaneous minimax estimation of parameters of multinomial distribution

95%
Trybuła S.
Applicationes Mathematicae
|
2002
|
tom 29
|
nr 3
307-311
EN
The problem of minimax estimation of parameters of multinomial distribution is considered for a loss function being the sum of the losses of the statisticians taking part in the estimation process.
9
Content available remote

A noisy duel under arbitrary moving. VI

36%
Trybuła S.
Applicationes Mathematicae
|
1991
|
tom 21
|
nr 1
83-98
10
Content available remote

A noisy duel under arbitrary moving. V

36%
Trybuła S.
Applicationes Mathematicae
|
1991
|
tom 21
|
nr 1
63-81
11
Content available remote

A noisy duel under arbitrary moving. IV

36%
Trybuła S.
Applicationes Mathematicae
|
1991
|
tom 21
|
nr 1
43-61
12
Content available remote

A silent duel under arbitrary moving

30%
Trybuła S.
Applicationes Mathematicae
|
1991
|
tom 21
|
nr 1
99-108
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