Search results for "likelihood"
showing 10 items of 264 documents
The “ThreePlusOne” Likelihood-Based Test Statistics: Unified Geometrical and Graphical Interpretations
2014
The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.
Inferential tools in penalized logistic regression for small and sparse data: A comparative study.
2016
This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…
The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing
2016
Abstract This paper refers to the problem stated by Balakrishnan et al. (2002). They proved that maximum likelihood estimator (MLE) of the exponential mean obtained from grouped samples is stochastically ordered provided that the sequence of the successive distances between inspection times is decreasing. In this paper we show that the assumption of monotonicity of the sequence of distances can be dropped.
Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns
2001
Plusieurs auteurs ont propose des approximations stochastiques et non-stochastiques au MLE pour les processus de Gibbs utilises pour decrire les interactions entre deux points dans une distribution spatiale de points. Cettes approximations sont necessaires a cause de la difficulte en l'evaluation de la constante qui normalise la f.d.p., Cet article present une comparaison, parmi d'un model de Strauss, des methodes qui utilisent des approximations directes aux MLE et des methodes qui utilisent techniques de Monte Carlo de chaine de Markov. Les techniques de simulation utilisees sont le Gibbs sampler et l'algorithm de Metropolis-Hastings.
Parameter orthogonality and conditional profile likelihood: the exponential power function case
1999
Orthogonality, according to Fisher’s metrics, between the parameters of a probability density function, as well as giving rise to a series of statistical implications, makes it possible to express a function of conditional profile likelihood with better properties than the ordinary profile likelihood function. In the present paper the parameters of exponential power function are made orthogonal and the conditional profile likelihood of the shape parameter p is determined in order to study its properties with reference to p estimation. Moreover, by means of a simulation plan, a comparison is made between the estimates of p obtained from the conditional profile log-likelihood and those obtain…
Selecting the tuning parameter in penalized Gaussian graphical models
2019
Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…
Sample size in cluster-randomized trials with time to event as the primary endpoint
2011
In cluster-randomized trials, groups of individuals (clusters) are randomized to the treatments or interventions to be compared. In many of those trials, the primary objective is to compare the time for an event to occur between randomized groups, and the shared frailty model well fits clustered time-to-event data. Members of the same cluster tend to be more similar than members of different clusters, causing correlations. As correlations affect the power of a trial to detect intervention effects, the clustered design has to be considered in planning the sample size. In this publication, we derive a sample size formula for clustered time-to-event data with constant marginal baseline hazards…
Structure Learning in Nested Effects Models
2007
Nested Effects Models (NEMs) are a class of graphical models introduced to analyze the results of gene perturbation screens. NEMs explore noisy subset relations between the high-dimensional outputs of phenotyping studies, e.g., the effects showing in gene expression profiles or as morphological features of the perturbed cell. In this paper we expand the statistical basis of NEMs in four directions. First, we derive a new formula for the likelihood function of a NEM, which generalizes previous results for binary data. Second, we prove model identifiability under mild assumptions. Third, we show that the new formulation of the likelihood allows efficiency in traversing model space. Fourth, we…
Stochastic ordering of classical discrete distributions
2010
For several pairs $(P,Q)$ of classical distributions on $\N_0$, we show that their stochastic ordering $P\leq_{st} Q$ can be characterized by their extreme tail ordering equivalent to $ P(\{k_\ast \})/Q(\{k_\ast\}) \le 1 \le \lim_{k\to k^\ast} P(\{k\})/Q(\{k\})$, with $k_\ast$ and $k^\ast$ denoting the minimum and the supremum of the support of $P+Q$, and with the limit to be read as $P(\{k^\ast\})/Q(\{k^\ast\})$ for $k^\ast$ finite. This includes in particular all pairs where $P$ and $Q$ are both binomial ($b_{n_1,p_1} \leq_{st} b_{n_2,p_2}$ if and only if $n_1\le n_2$ and $(1-p_1)^{n_1}\ge(1-p_2)^{n_2}$, or $p_1=0$), both negative binomial ($b^-_{r_1,p_1}\leq_{st} b^-_{r_2,p_2}$ if and on…
An extended continuous mapping theorem for outer almost sure weak convergence
2019
International audience; We prove an extended continuous mapping theorem for outer almost sure weak convergence in a metric space, a notion that is used in bootstrap empirical processes theory. Then we make use of those results to establish the consistency of several bootstrap procedures in empirical likelihood theory for functional parameters.