scholarly journals A study of the power and robustness of a new test for independence against contiguous alternatives

2016 ◽  
Vol 10 (1) ◽  
pp. 330-351 ◽  
Author(s):  
Subhra Sankar Dhar ◽  
Angelos Dassios ◽  
Wicher Bergsma
Keyword(s):  
Contiguous Alternatives

Conditional likelihood and power: higher-order asymptotics

1992 ◽  
Vol 438 (1904) ◽  
pp. 433-446 ◽  
Keyword(s):  
Average Power ◽  
Nuisance Parameter ◽  
Second Order ◽  
Conditional Likelihood ◽  
Power Functions ◽  
Third Order ◽  
Contiguous Alternatives ◽  
Higher Order Asymptotics ◽  
Optimality Property ◽  
Lr Test

This paper considers, in the presence of a nuisance parameter, a very large class of tests that includes the conditional and the usual versions of the likelihood ratio (LR), Rao’s and Wald’s tests. Under contiguous alternatives and orthogonal parametrization, the power functions of the conditional and the usual versions of these tests have been compared and, in particular, it is seen that the power functions of the conditional versions, unlike those of the usual versions, are identical, up to the second-order, with the power functions of the corresponding tests with known nuisance parameter. An optimality property of the conditional LR test, in terms of second-order local maximinity, has been established. A test, optimal in the sense of third-order average power under contiguous alternatives, has been proposed. A weaker optimality property of Rao’s test, in terms of third-order average power, has also been indicated.

Asymptotic distributions of weighted pontograms under contiguous alternatives

1992 ◽  
Vol 112 (2) ◽  
pp. 431-447 ◽  
Author(s):  
Barbara Szyszkowicz
Keyword(s):  
Poisson Process ◽  
Density Function ◽  
Null Hypothesis ◽  
Asymptotic Distributions ◽  
Contiguous Alternatives

Let {N(x), x ≥ 0} be a non-homogeneous, also called non-stationary, Poisson process with density function λ(x), x ≥ 0. We consider the problem of testing the null hypothesis of λ(x) having a constant value against the alternative that λ(x) is a function of x.

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