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Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model

Gejza Wimmer (1995)

Applications of Mathematics

The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.

Robustez cualitativa en regiones de confianza.

Antonio Cuevas, Paloma Sanz (1990)

Trabajos de Estadística

In this paper, Hampel's concept of qualitative robustness (1968, 1971) is adapted to the problem of estimation by confidence regions. The basic idea is to consider the confidence regions as generalized estimates taking values in the space of compact sets endowed with the Hausdorff metric.In section 3, the qualitative robustness is analyzed in five particular cases, which include confidence regions and tolerance intervals of common use. Section 4 is devoted to discussion and comments.

Sample size and tolerance limits.

Milos Jilek (1982)

Trabajos de Estadística e Investigación Operativa

Several new criteria are proposed for the determination of suitable sample size for assessing the statistical tolerance limits. The application of the criteria is illustrated on the solution of some problems from the theory of errors and theory of reliability.

Scaling of model approximation errors and expected entropy distances

Guido F. Montúfar, Johannes Rauh (2014)

Kybernetika

We compute the expected value of the Kullback-Leibler divergence of various fundamental statistical models with respect to Dirichlet priors. For the uniform prior, the expected divergence of any model containing the uniform distribution is bounded by a constant 1 - γ . For the models that we consider this bound is approached as the cardinality of the sample space tends to infinity, if the model dimension remains relatively small. For Dirichlet priors with reasonable concentration parameters the expected...

Sensitivity analysis in singular mixed linear models with constraints

Eva Fišerová, Lubomír Kubáček (2003)

Kybernetika

The singular mixed linear model with constraints is investigated with respect to an influence of inaccurate variance components on a decrease of the confidence level. The algorithm for a determination of the boundary of the insensitivity region is given. It is a set of all shifts of variance components values which make the tolerated decrease of the confidence level only. The problem about geometrical characterization of the confidence domain is also presented.

Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

František Rublík (2001)

Kybernetika

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...

The shortest randomized confidence interval for probability of success in a negative binomial model

Wojciech Zieliński (2014)

Applicationes Mathematicae

Zieliński (2012) showed the existence of the shortest confidence interval for a probability of success in a negative binomial distribution. The method of obtaining such an interval was presented as well. Unfortunately, the confidence interval obtained has one disadvantage: it does not keep the prescribed confidence level. In the present article, a small modification is introduced, after which the resulting shortest confidence interval does not have that disadvantage.

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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