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Previous European guidance for environmental risk assessment of genetically
modified plants emphasized the concepts of statistical power but provided no
explicit requirements for the provision of statistical power analyses.
Similarly, whilst the need for good experimental designs was stressed, no
minimum guidelines were set for replication or sample sizes. Furthermore,
although substantial equivalence was stressed as central to risk assessment,
no means of quantification of this concept was given. This paper suggests
several ways in which existing guidance might be revised to address these
problems. One approach explored is the `bioequivalence' test, which has the
advantage that the error of most concern to the consumer may be set
relatively easily. Also, since the burden of proof is placed on the
experimenter, the test promotes high-quality, well-replicated experiments
with sufficient statistical power.
Other recommendations cover the specification of effect sizes, the choice of
appropriate comparators, the use of positive controls, meta-analyses,
multivariate analysis and diversity indices. Specific guidance is suggested
for experimental designs of field trials and their statistical analyses. A
checklist for experimental design is proposed to accompany all environmental
A method is introduced to select the significant or non null mean terms among a collection
of independent random variables. As an application we consider the problem of
significant coefficients in non ordered model selection. The method is based on a convenient random centering of
the partial sums of the ordered observations. Based on
L-statistics methods we show consistency of the proposed
An extension to unknown parametric distributions is considered.
examples are included to show the accuracy of the estimator.
An example of signal denoising with wavelet thresholding is also discussed.
The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is
a powerful alternative to EM when the E-step is intractable. Convergence of
SAEM toward a maximum of the observed likelihood is established when
the unobserved data are simulated at each iteration under the conditional
distribution. We show that this very restrictive assumption can be weakened. Indeed,
the results of Benveniste et al. for stochastic approximation
with Markovian perturbations are used to establish the convergence
of SAEM when it is coupled with a Markov chain Monte-Carlo
procedure. This result is very useful for many practical applications.
Applications to the convolution model and the change-points model are presented to illustrate the proposed method.
Under regularity assumptions, we establish a sharp large
deviation principle for Hermitian quadratic forms of
stationary Gaussian processes. Our result is similar to
the well-known Bahadur-Rao theorem  on the sample
mean. We also provide several examples of application
such as the sharp large deviation properties of
the Neyman-Pearson likelihood ratio test, of the sum of squares,
of the Yule-Walker
estimator of the parameter of a stable autoregressive Gaussian process,
and finally of the empirical spectral repartition function.
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