A Complete Class of Tests when the Likelihood is Locally Asymptotically Quadratic
نویسنده
چکیده
This paper constructs an asymptotically complete class of tests (i.e. for a test not within this class one can ...nd a test within the class that has better or equal asymptotical powerfunction) for testing one parametric restriction when the likelihoodfunction can asymptotically be approximated by a quadratic function: The coe¢cients of this quadratic form may be random variables, so that our results also apply to the problem of unit-root testing.
منابع مشابه
Optimal Estimation under Nonstandard Conditions
We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Camoptimality theory is adapted to cover this situation.We show that the expect...
متن کاملCenter manifold analysis and Hopf bifurcation of within-host virus model
A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...
متن کاملHypotheses Testing: Poisson versus Self-correcting
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a self-correcting point process. The underlying family of measures is locally asymptotically quadratic and we describe the behavior of score function, likelihoo...
متن کاملHypotheses Testing: Poisson Versus Stress-release
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a self-correcting point process. The underlying family of measures is locally asymptotically quadratic and we describe the behavior of score function, likelihoo...
متن کاملOptimal tests for homogeneity of covariance, scale, and shape
The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic context of multivariate Gaussian models. And the modified likelihood ratio tests (MLRT) that are used ...
متن کامل