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Minimax mutual prediction

Stanisław Trybuła (2000)

Applicationes Mathematicae

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.

Minimax mutual prediction of multinomial random variables

Stanisław Trybuła (2003)

Applicationes Mathematicae

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.

Minimax nonparametric prediction

Maciej Wilczyński (2001)

Applicationes Mathematicae

Let U₀ be a random vector taking its values in a measurable space and having an unknown distribution P and let U₁,...,Uₙ and V , . . . , V m be independent, simple random samples from P of size n and m, respectively. Further, let z , . . . , z k be real-valued functions defined on the same space. Assuming that only the first sample is observed, we find a minimax predictor d⁰(n,U₁,...,Uₙ) of the vector Y m = j = 1 m ( z ( V j ) , . . . , z k ( V j ) ) T with respect to a quadratic errors loss function.

Minimax Prediction for the Multinomial and Multivariate Hypergeometric Distributions

Alicja Jokiel-Rokita (1998)

Applicationes Mathematicae

A problem of minimax prediction for the multinomial and multivariate hypergeometric distribution is considered. A class of minimax predictors is determined for estimating linear combinations of the unknown parameter and the random variable having the multinomial or the multivariate hypergeometric distribution.

Minimax prediction under random sample size

Alicja Jokiel-Rokita (2002)

Applicationes Mathematicae

A class of minimax predictors of random variables with multinomial or multivariate hypergeometric distribution is determined in the case when the sample size is assumed to be a random variable with an unknown distribution. It is also proved that the usual predictors, which are minimax when the sample size is fixed, are not minimax, but they remain admissible when the sample size is an ancillary statistic with unknown distribution.

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