Technique for detecting the presence of finite sample‐size effects in transmitted‐wave measurements made on multilayer underwater acoustic panels

1991 ◽  
Vol 90 (5) ◽  
pp. 2831-2842 ◽  
Author(s):  
Jean C. Piquette
Keyword(s):  
Sample Size ◽  
Size Effects ◽  
Transmitted Wave ◽  
Finite Sample ◽  
Underwater Acoustic ◽  
Wave Measurements ◽  
Finite Sample Size

scholarly journals Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

2017 ◽  
Vol 95 (24) ◽  
Author(s):  
Miguel Camacho ◽  
Rafael R. Boix ◽  
Francisco Medina ◽  
Alastair P. Hibbins ◽  
J. Roy Sambles
Keyword(s):  
Sample Size ◽  
Surface Waves ◽  
Size Effects ◽  
Finite Sample ◽  
Slot Arrays ◽  
Finite Sample Size

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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