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...
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
recovering the
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
-statistics methods we show consistency of the proposed
estimator.
An extension to unknown parametric distributions is considered.
Simulated
examples...
The stochastic approximation version of EM (SAEM) proposed by Delyon (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 for stochastic approximation
with Markovian perturbations are used to establish the convergence
of...
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 [2] 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...
Download Results (CSV)