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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...
We study the LRT statistic for testing
a single population i.i.d. model against a mixture of two populations with Markov regime.
We prove that
the LRT statistic converges to infinity in probability
as the number of observations tends to infinity.
This is a consequence of a convergence result
of the LRT statistic for a subproblem where the parameters
are restricted to a subset of the whole parameter set.
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