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Sequential estimation in processes with independent increments

100%

Trybuła S.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction...................... 5 2. Definitions........................... 6 3. Stochastic processes.................. 7 4. Processes with independent increments...... 8 5. Sequential estimation for the Poisson process..... 12 6. Other processes with independent increments.......... 33 7. Efficiency for a given value of the parameter......... 39 8. Final remarks........................................... 43 References................................................ 45

2

Ocena frekwencji w populacji elementów należących do klas niereprezentowanych w próbce

94%

Trybuła S.

Applicationes Mathematicae

|

1958-1959

|

tom 4

|

nr 3

244-248

3

Estymacja z uwzględnieniem błędów kontrolera

71%

Trybuła S.

Applicationes Mathematicae

|

1958-1959

|

tom 4

|

nr 3

249-254

4

Sequential estimation in finite-state Markov processes

71%

Trybuła S.

Applicationes Mathematicae

|

1980-1983

|

tom 17

|

nr 2

227-248

5

Oblique plans for a binomial process

60%

Magiera R., Trybuła S.

Mathematica Applicanda

|

1976

|

tom 4

|

nr 6

EN

The following random walk (Xt, t=0,1,2,⋯) in the set T= {(x,y):x,y are nonnegative integers} is considered: X0=(0,0), Prob{Xt+1=(x+1,y)|Xt=(x,y)}==1-Prob{Xt+1=(x,y+1)|Xt=p(x,y)}, p∈(0,1) being unknown. For a given B⊂T, define the stopping variable τ=min{t>0:Xt∈B}. A sequential procedure of estimation of a parameter Q=g(p) by a function f(Xτ,τ) is said to be an oblique plan if B is of the form {(x,y):y=(x-k)/s}, where k and s are positive integers. Some properties of estimates in oblique plans are discussed. .

6

Dual control for disturbances with Poisson distribution

59%

Trybuła S.

Applicationes Mathematicae

|

1972-1973

|

tom 13

|

nr 2

159-164

7

On the paradox of n random variables

59%

Trybuła S.

Applicationes Mathematicae

|

1965

|

tom 8

|

nr 2

143-156

8

Minimax prediction of a sample distribution function

59%

Trybuła S.

Applicationes Mathematicae

|

1977-1980

|

tom 16

|

nr 2

167-174

9

On the paradox of three random variables

59%

Trybuła S.

Applicationes Mathematicae

|

1960-1961

|

tom 5

|

nr 4

321-332

10

Minimax control of a stochastic system with disturbances belonging to the exponential family

48%

Trybuła S., Szajowski K.

Applicationes Mathematicae

|

1983-1985

|

tom 18

|

nr 4

525-539

11

Minimax estimation of the parameters of the multivariate hypergeometric distribution

47%

Trybuła S.

Applicationes Mathematicae

|

1983-1985

|

tom 18

|

nr 4

559-570

12

Minimax estimation of a cumulative distribution function for a special loss function

47%

Trybuła S.

Applicationes Mathematicae

|

1991

|

tom 21

|

nr 4

555-560

13

An m-vs.-n-bullets silent duel with arbitrary motion and arbitrary accuracy functions

47%

Trybuła S.

Applicationes Mathematicae

|

1991

|

tom 21

|

nr 4

545-554

14

Minimax control of a multivariate time-continuous linear stochastic system

47%

Trybuła S.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 2

225-238

15

Minimax estimation and prediction for random variables with bounded sum

47%

Trybuła S.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 1

85-91

16

Solution of some problems of minimax control for a multivariate linear stochastic system

47%

Trybuła S.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 2

203-223

17

Minimax control of a linear system with multinomial disturbances

42%

Trybuła S.

Applicationes Mathematicae

|

1988

|

tom 20

|

nr 1

67-81

18

Minimax and Bayes estimation when the loss function is unknown

42%

Trybuła S.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 1

69-83

19

Two problems of minimax estimation

42%

Trybuła S.

Applicationes Mathematicae

|

1974-1975

|

tom 14

|

nr 2

195-204

20

Some problems of prediction of the difference of random variables

42%

Trybuła S.

Applicationes Mathematicae

|

1991

|

tom 21

|

nr 2

153-159

Ograniczanie wyników

Sequential estimation in processes with independent increments

Ocena frekwencji w populacji elementów należących do klas niereprezentowanych w próbce

Estymacja z uwzględnieniem błędów kontrolera

Sequential estimation in finite-state Markov processes

Oblique plans for a binomial process

Dual control for disturbances with Poisson distribution

On the paradox of n random variables

Minimax prediction of a sample distribution function

On the paradox of three random variables

Minimax control of a stochastic system with disturbances belonging to the exponential family

Minimax estimation of the parameters of the multivariate hypergeometric distribution

Minimax estimation of a cumulative distribution function for a special loss function

An m-vs.-n-bullets silent duel with arbitrary motion and arbitrary accuracy functions

Minimax control of a multivariate time-continuous linear stochastic system

Minimax estimation and prediction for random variables with bounded sum

Solution of some problems of minimax control for a multivariate linear stochastic system

Minimax control of a linear system with multinomial disturbances

Minimax and Bayes estimation when the loss function is unknown

Two problems of minimax estimation

Some problems of prediction of the difference of random variables