Asymptotic Considerations for Selecting the Best Component of a Multivariate Normal Population.
Asymptotic distribution of the conditional regret risk for selecting good exponential populations
In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang [10] who proved that the regret risk converges to zero with rate . The aim of this paper is to study the asymptotic behavior of the conditional regret risk . It is shown that tends in distribution to a linear combination of independent -distributed random variables. As an application we...
Asymptotic distribution of the likelihood ratio test statistic in the multisample case
Asymptotic efficiency and robustness of -estimators
Asymptotic Expansion of the Power Function of the Two-Sample Binomial Test with and without Randomization.
Asymptotic expansions of functions of statistics
Asymptotic normality and efficiency of variance components estimators with high breakdown points
For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of...
Asymptotic normality of randomly truncated stochastic algorithms
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly...
Asymptotic optimality of sequential designs for estimation.
Asymptotic optimality of the Bayes estimator on differentiable in quadratic mean models.
Asymptotic properties of autoregressive regime-switching models
The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent...
Asymptotic properties of autoregressive regime-switching models
The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent...
Asymptotic Properties of Minimum Contrast Estimators for Parameters of Boolean Models.
Asymptotic properties of the growth curve model with covariance components
We consider a multivariate regression (growth curve) model of the form , , , where and ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters estimating simultaneously the first and the second order parameters.
Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes
We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate the inhomogeneity...
Asymptotic results in parameter estimation for Gibbs random fields
Asymptotic separation in bilinear models.
Asymptotic stability of tests based on order statistics for the scale parameter
Asymptotic theory of parameter estimation for Gauss-Markov random fields
Asymptotical confidence region in a replicated mixed linear model with an estimated covariance matrix