On asymptotic minimaxity of kernel-based tests

Michael Ermakov

Displaying similar documents to “On asymptotic minimaxity of kernel-based tests”

A class of tests for exponentiality based on a continuum of moment conditions

Simos G. Meintanis (2009)

Kybernetika

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The empirical moment process is utilized to construct a family of tests for the null hypothesis that a random variable is exponentially distributed. The tests are consistent against the 'new better than used in expectation' (NBUE) class of alternatives. Consistency is shown and the limit null distribution of the test statistic is derived, while efficiency results are also provided. The finite-sample properties of the proposed procedure in comparison to more standard procedures are investigated...

Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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Existence results are established for the resonant problem $y^{''} + λ_{m} a y = f (t, y)$ a.e. on $[0, 1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a \in L_{l o c}^{1} (0, 1)$ with $a > 0$ a.e. on $[0, 1]$ and $\int_{0}^{1} x (1 - x) a (x) d x < \infty$ .

Resolvents, integral equations, limit sets

Theodore Allen Burton, D. P. Dwiggins (2010)

Mathematica Bohemica

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In this paper we study a linear integral equation $x (t) = a (t) - \int_{0}^{t} C (t, s) x (s) d s$ , its resolvent equation $R (t, s) = C (t, s) - \int_{s}^{t} C (t, u) R (u, s) d u$ , the variation of parameters formula $x (t) = a (t) - \int_{0}^{t} R (t, s) a (s) d s$ , and a perturbed equation. The kernel, $C (t, s)$ , satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of $C$ and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.

On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties

František Rublík (2007)

Kybernetika

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Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities....

Criteria for disfocality and disconjugacy for third order differential equations.

Panigrahi, S. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Goodness-of-fit tests for parametric regression models based on empirical characteristic functions

Marie Hušková, Simon G. Meintanis (2009)

Kybernetika

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Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical...