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Two-point priors and minimax estimation of a bounded parameter under convex loss

Agata Boratyńska (2005)

Applicationes Mathematicae

The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

Two-sample rank tests based on exceeding observations

Eugenia Stoimenova (2007)

Applications of Mathematics

Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s E -test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics.

Two-sided Tolerance Intervals in a Simple Linear Regression

Martina Chvosteková (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested...

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