Lien non spécifié dans les modèles linéaires généralisés
Likelihood and parametric heteroscedasticity in normal connected linear models
A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
Likelihood and quasi - likelihood estimation of transition probabilities
In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.
Likelihood and the Bayes procedure.
In this paper the likelihood function is considered to be the primary source of the objectivity of a Bayesian method. The necessity of using the expected behaviour of the likelihood function for the choice of the prior distribution is emphasized. Numerical examples, including seasonal adjustment of time series, are given to illustrate the practical utility of the common-sense approach to Bayesian statistics proposed in this paper.
Likelihood for interval-censored observations from multi-state models.
We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed bivariate counting...
Likelihood for random-effect models (with discussion).
For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows influence from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and discuss why...
Likelihood ratio inequalities with applications to various mixtures
Likelihood ratio rank tests for the two-sample problem with randomly censored data
Liminary on Guilbaud's 1952 paper.
Limit distribution of the integrated squared error of trigonometric series regression estimator.
Limit distribution of the mean square deviation of the Gasser-Müller nonparametric estimate of the regression function.
Limit distributions of quantiles for a random sample of random length
Limit state analysis on the un-repeated multiple selection bounded confidence model
In this paper, we study the opinion evolution over social networks with a bounded confidence rule. Node initial opinions are independently and identically distributed. At each time step, each node reviews the average opinions of several different randomly selected agents and updates its opinion only when the difference between its opinion and the average is below a threshold. First of all, we provide probability bounds of the opinion convergence and the opinion consensus, are both nontrivial events...
Limit theorem for random walk in weakly dependent random scenery
Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.
Limit theorems for Banach-valued autoregressive processes. Applications to real continuous time processes.
Limit theorems for bivariate extremes of non-identically distributed random variables
The limit behaviour of the extreme order statistics arising from n two-dimensional independent and non-identically distributed random vectors is investigated. Necessary and sufficient conditions for the weak convergence of the distribution function (d.f.) of the vector of extremes, as well as the form of the limit d.f.'s, are obtained. Moreover, conditions for the components of the vector of extremes to be asymptotically independent are studied.
Limit theorems for Pareto-type distributions
Limit theorems for rank statistics detecting gradual changes
The purpose of the paper is to investigate weak asymptotic behaviour of rank statistics proposed for detection of gradual changes, linear trends in particular. The considered statistics can be used for various test procedures. The fundaments of the proofs are formed by results of Hušková [4] and Jarušková [5].
Limit theorems for self-normalized large deviation.
Limit theorems for stationary Markov processes with L2-spectral gap
Let be a discrete or continuous-time Markov process with state space where is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. is assumed to be a Markov additive process. In particular, this implies that the first component is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process is shown to satisfy the...