scholarly journals Poisson process and distribution-free statistics

1974 ◽  
Vol 6 (2) ◽  
pp. 359-375 ◽  
Author(s):  
Meyer Dwass
Keyword(s):  
Poisson Process ◽  
Sample Size ◽  
Point Of View ◽  
Finite Sample ◽  
Qualitative Information ◽  
Distribution Free ◽  
Finite Sample Size

The well-known connection between the Poisson process and empirical c.d.f.'s is exploited from a new point of view. Distributions of functions of empirical c.d.f.'s for finite sample size n are explicitly described in some new examples, and new qualitative information is obtained for some classical examples.

scholarly journals Poisson process and distribution-free statistics

1974 ◽  
Vol 6 (02) ◽  
pp. 359-375 ◽  
Author(s):  
Meyer Dwass
Keyword(s):  
Poisson Process ◽  
Sample Size ◽  
Point Of View ◽  
Finite Sample ◽  
Qualitative Information ◽  
Distribution Free ◽  
Finite Sample Size

The well-known connection between the Poisson process and empirical c.d.f.'s is exploited from a new point of view. Distributions of functions of empirical c.d.f.'s for finite sample size n are explicitly described in some new examples, and new qualitative information is obtained for some classical examples.

scholarly journals On the variance parameter estimator in general linear models

Metrika ◽  
2019 ◽  
Vol 83 (2) ◽  
pp. 243-254
Author(s):  
Mathias Lindholm ◽  
Felix Wahl
Keyword(s):  
Sample Size ◽  
Linear Models ◽  
General Linear ◽  
Finite Sample ◽  
Parameter Estimator ◽  
General Linear Models ◽  
Vector Autoregressive ◽  
Finite Sample Size ◽  
Error Terms ◽  
Variance Parameter

Abstract In the present note we consider general linear models where the covariates may be both random and non-random, and where the only restrictions on the error terms are that they are independent and have finite fourth moments. For this class of models we analyse the variance parameter estimator. In particular we obtain finite sample size bounds for the variance of the variance parameter estimator which are independent of covariate information regardless of whether the covariates are random or not. For the case with random covariates this immediately yields bounds on the unconditional variance of the variance estimator—a situation which in general is analytically intractable. The situation with random covariates is illustrated in an example where a certain vector autoregressive model which appears naturally within the area of insurance mathematics is analysed. Further, the obtained bounds are sharp in the sense that both the lower and upper bound will converge to the same asymptotic limit when scaled with the sample size. By using the derived bounds it is simple to show convergence in mean square of the variance parameter estimator for both random and non-random covariates. Moreover, the derivation of the bounds for the above general linear model is based on a lemma which applies in greater generality. This is illustrated by applying the used techniques to a class of mixed effects models.

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