Introduction de la notion d'écart entre sous-espaces vectoriels en analyse de données
Invalid permutation tests.
Invariance and R-ε criterion.
The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ1, ..., θn}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible...
Invariance of Covariance Structures Under Groups of Transformations.
Invariance principle in a bilinear model with weak nonlinearity.
Invariance principles for absolutely regular empirical processes
Invariance principles in Hölder spaces.
Invariancia de las reglas admisibles y Bayes respecto de transformaciones monótonas.
From an optimality point of view the solution of a decision problem is related to classes of optimal strategies: admissible, Bayes, etc. which are closely related to boundaries of the risk set S such as lower-boundary, Bayes boundary, positive Bayes boundary. In this paper we present some results concerning invariance properties of such boundaries when the set is transformed by means of a continuous monotonic increasing function W.
Invariant copulas
Invariant Density Estimation.
Invariant measures of the pair: state, approximate filtering process
Inverse Cauchy problem and unbiased estimation
Inverse distributions: the logarithmic case
In this paper it is proved that the distribution of the logarithmic series is not invertible while it is found to be invertible if corrected by a suitable affinity. The inverse distribution of the corrected logarithmic series is then derived. Moreover the asymptotic behaviour of the variance function of the logarithmic distribution is determined. It is also proved that the variance function of the inverse distribution of the corrected logarithmic distribution has a cubic asymptotic behaviour.
Inverse sampling and triangular sequential designs to compare a small proportion with a reference value.
Inverse sampling and formal sequential designs may prove useful in reducing the sample size in studies where a small population proportion p is compared with a hypothesized reference proportion p0. These methods are applied to the design of a cytogenetic study about chromosomal abnormalities in men with a daughter affected by Turner's syndrome. First it is shown how the calculated sample size for a classical design depends on the parameterization used. Later this sample size is compared with the...
Inversion of partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters
The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation...
Inversions en classification hiérarchique : application à la construction adaptative d'indices d'agrégation
Inverting covariance matrices
Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.
Investigation of periodicity for dependent observations
It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.
Invited paper with discussion: Natural Induction: An objective Bayesian approach.
Irregular sampling and central limit theorems for power variations : the continuous case
In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on...