Nonparametric multivariate rank tests and their unbiasedness

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17 (1965) 261--263]; he found an alternative against which the Wilcoxon test is not unbiased. The problem is even more serious in multivariate models. When testing the hypothesis against an alternative which fits well with the experiment, it should be verified whether the power of the test under this alternative cannot be smaller than the significance level. Surprisingly, this serious problem is not frequently considered in the literature. The present paper considers the two-sample multivariate testing problem. We construct several rank tests which are finite-sample unbiased against a broad class of location/scale alternatives and are finite-sample distribution-free under the hypothesis and alternatives. Each of them is locally most powerful against a specific alternative of the Lehmann type. Their powers against some alternatives are numerically compared with each other and with other rank and classical tests. The question of affine invariance of two-sample multivariate tests is also discussed.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ326 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests

The paper evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for beta-mixing processes and EDF-based tests for the residuals of such nonlinear dependent processes. Hence the tests apply to the class of ARCH and SV type processes as well as data-driven volatility estimators using high-frequency data. It is shown that some of the high-frequency volatility estimators substantially improve the power of the structural breaks tests especially for detecting changes in the tail of the conditional distribution. Similarly, certain types of filtering and transformation of the returns process can improve the power of CUSUM statistics. We also explore the impact of sampling frequency on each of the test statistics. Ce papier évalue la performance de plusieurs tests de changement structurel CUSUM et EDF pour la structure dynamique de la variance conditionelle et de la distribution conditionnelle. Nous étudions l'impact 1) de la fréquence des observations, 2) de l'utilisation des données de haute fréquence pour le calcul des variances conditionnelles et 3) de transformation des séries pour améliorer la puissance des tests.Change-point tests, CUSUM, Kolmogorov-Smirnov, GARCH, quadratic variation, power variation, high-frequency data, location-scale distribution family, tests de changement structurel, CUSUM, Kolmogov-Smirnov, GARCH, variation quadratique, 'power variation', données de haute fréquence

Consistent tests of conditional moment restrictions

We propose two classes of consistent tests in parametric econometric models defined through multiple conditional moment restrictions. The first type of tests relies on nonparametric estimation, while the second relies on a functional of a marked empirical process. For both tests, a simulation procedure for obtaining critical values is shown to be asymptotically valid. Finite sample performances of the tests are investigated by means of several Monte-Carlo experiments.Publicad

New goodness-of-fit diagnostics for conditional discrete response models

This paper proposes new specification tests for conditional models with discrete responses, which are key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events. In particular, we test the static and dynamic ordered choice model specifications and can cover infinite support distributions for e.g. count data. The traditional approach for specification testing of discrete response models is based on probability integral transforms of a jittered discrete data which leads to continuous uniform iid series under the true conditional distribution. Then, standard specification testing techniques for continuous variables could be applied to the transformed series, but the extra randomness from jitters affects the power properties of these methods. We investigate in this paper an alternative transformation based only on original discrete data that avoids any randomization. We analyze the asymptotic properties of goodness-of-fit tests based on this new transformation and explore the properties in finite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent. We show analytically and in simulations that our approach dominates the methods based on randomization in terms of power. We apply the new tests to models of the monetary policy conducted by the Federal Reserve