Search results for " normality"
showing 6 items of 16 documents
Affine-invariant rank tests for multivariate independence in independent component models
2016
We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…
A note on finite PST-groups
2007
[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, for subgroups H and K of G with H normal in K and K normal in G, it is always the case that H is Sylow-permutable in G. In this paper, we show that finite PST-groups and finite T*-groups are one and the same. A new characterisation of soluble PST-groups is also presented.
A more efficient second order blind identification method for separation of uncorrelated stationary time series
2016
The classical second order source separation methods use approximate joint diagonalization of autocovariance matrices with several lags to estimate the unmixing matrix. Based on recent asymptotic results, we propose a novel unmixing matrix estimator which selects the best lag set from a finite set of candidate sets specified by the user. The theory is illustrated by a simulation study. peerReviewed
Extracting Conditionally Heteroskedastic Components using Independent Component Analysis
2020
In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coef…
KERNEL ESTIMATION OF THE TRANSITION DENSITY IN BIFURCATING MARKOV CHAINS
2023
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods are based on the so-called two bandwidths approach.
Model selection using limiting distributions of second-order blind source separation algorithms
2015
Signals, recorded over time, are often observed as mixtures of multiple source signals. To extract relevant information from such measurements one needs to determine the mixing coefficients. In case of weakly stationary time series with uncorrelated source signals, this separation can be achieved by jointly diagonalizing sample autocovariances at different lags, and several algorithms address this task. Often the mixing estimates contain close-to-zero entries and one wants to decide whether the corresponding source signals have a relevant impact on the observations or not. To address this question of model selection we consider the recently published second-order blind identification proced…