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This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled...
This paper derives an explicit approximation for the tail probability of a sum of sample
values taken without replacement from an unrestricted finite population. The approximation
is shown to hold under no conditions in a wide range with relative error given in terms of
the standardized absolute third moment of the population, β3N. This approximation is used to obtain
a result comparable to the well-known Cramér large deviation result in the independent
...
The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...
This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be -consistent for all values of the long memory parameters...
In the paper a test of the hypothesis , on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
In this paper, we address the problem of testing hypotheses
using maximum likelihood statistics in non identifiable models.
We derive the asymptotic distribution under very general assumptions.
The key idea is a local reparameterization, depending on the underlying
distribution, which is called locally conic. This method enlights how
the general model induces the structure of the limiting distribution
in terms of dimensionality of some derivative space. We present various
applications of...
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...
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