Lois limites du Bootstrap de certaines fonctionnelles
Lois limites et efficacité asymptotique des tests hilbertiens de dimension finie sous des hypothèses adjacentes
Max-type rank tests in the two-sample problem
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
We observe an infinitely dimensional Gaussian random vector x = ξ + v where ξ is a sequence of standard Gaussian variables and v ∈ l2 is an unknown mean. We consider the hypothesis testing problem H0 : v = 0versus alternatives for the sets . The sets Vε are lq-ellipsoids of semi-axes ai = i-s R/ε with lp-ellipsoid of semi-axes bi = i-r pε/ε removed or similar Besov bodies Bq,t;s (R/ε) with Besov bodies Bp,h;r (pε/ε) removed. Here or are the parameters which define the sets Vε for given radii...
New estimates and tests of independence in semiparametric copula models
We introduce new estimates and tests of independence in copula models with unknown margins using -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of -divergence has good properties in terms of efficiency-robustness.
New results on the NBUFR and NBUE classes of life distributions
Some properties of the "new better than used in failure rate" (NBUFR) and the "new better than used in expectation" (NBUE) classes of life distributions are given. These properties include moment inequalities and moment generating functions behaviors. In addition, nonparametric estimation and testing of the survival functions of these classes are discussed.
New variance ratio tests to identify random walk from the general mean reversion model.
Nonparametric analysis of blocked ordered categories data: Some examples revisited.
Nonparametric tests for data in randomised blocks with ordered alternatives.
Normalité asymptotique d'une classe de statistiques de rangs sérielles multivariées
Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality
Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.
Normalizing constants for a statistic based on logarithms of disjoint m-spacings
The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
Note on Sign Tests for Equality of Means of k Bivariate Populations.
Note on the Kolmogorov Statistic for a General Discontinuous Variable.
On a class of distribution-free tests for growth curves analyses
On a robust significance test for the Cox regression model
A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.
On Approximating the Distributions of Friedman's xr2 and Related Statistics.
On asymptotic minimaxity of kernel-based tests
In the problem of signal detection in gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal -norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the -norms of signal smoothed by the kernels exceed some constants . The constant depends on the power of noise and as . Similar statements are proved also if an additional information on a signal smoothness is given....
On Asymptotic Minimaxity of Kernel-based Tests
In the problem of signal detection in Gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal L2-norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the L2-norms of signal smoothed by the kernels exceed some constants pε > 0. The constant pε depends on the power ϵ of noise and pε → 0 as ε → 0. Similar statements are proved also if an additional information on a signal...