Testing in locally conic models, and application to mixture models
Testing in locally conic models, and application to mixture models
In this paper, we address the problem of testing hypotheses using maximum likelihood statistics in non identifiable models. We derive the asymptotic distribution under very general assumptions. The key idea is a local reparameterization, depending on the underlying distribution, which is called locally conic. This method enlights how the general model induces the structure of the limiting distribution in terms of dimensionality of some derivative space. We present various applications of...
Testing in stationary models based on divergences of observed and theoretical frequencies
Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility
Stochastic Volatility (SV) models are widely used in financial applications. To decide whether standard parametric restrictions are justified for a given data set, a statistical test is required. In this paper, we develop such a test of a linear hypothesis versus a general composite nonparametric alternative using the state space representation of the SV model as an errors-in-variables AR(1) model. The power of the test is analyzed. We provide a simulation study and apply the test to the HFDF96...
Testing the independence of two Poisson processes.
Testing Whether F is More IFR than G .
Tests derived from characterizations in terms of moments of record values
We derive tests of fit from characterizations of continuous distributions via moments of the kth upper record values.
Tests of fit for the logarithmic distribution.
Tests of independence of normal random variables with known and unknown variance ratio
In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between...
Tests of Significance for the Average Square Deviation from Target in a Finite Lot.
Tests simultanés de permutation des rangs pour bruit-blanc multivarié
The Berry-Esseen theorem for rank statistics
The distribution of the estimate of entropy and its applications
The infinitesimal robustness of tests against dependence
The Large-Sample Power of the x Test fox Multidimensional Contingency Tables.
The likelihood ratio test for general mixture models with or without structural parameter
This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations...
The Minimum Distance Method of Testing.
The most significant interaction in a contingency table
The multisample version of the Lepage test
The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of sampled populations. It is shown that its limiting distribution is the chi-square distribution with degrees of freedom. This -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular...
The robustness against dependence of nonparametric tests for the two-sample location problem
Nonparametric tests for the two-sample location problem are investigated. It is shown that the supremum of the size of any test can be arbitrarily close to 1. None of these tests is most robust against dependence.