1,721,321 research outputs found
Robust conditional inference for location parameters.
Full text linkThe robustness properties of conditional normal-theory procedures of inference for a location parameter are considered; in particular, a robust conditional density is proposed to be used instead of the classical methods based on the assumption of normality. The new density is conditional on a robust ancillary and its properties are studied in comparison to the exact conditional density but also under slight violations of the normal model assumption
Higher-order approximations for Pitman estimators and for optimal compromise estimators
No full textLaplace approximations for the Pitman estimators of location or scale parameters, including terms O(n-l), are obtained. The resulting expressions involve the maximum-likelihood estimate
and the derivatives of the log-likelihood function up to order 3. The results can be used to refine the approximations for the optimal compromise estimators for location parameters considered by Easton (199 I). Some applications and Monte Carlo simulations are discussed
Use of approximate marginal likelihood for model selection.
No full textOptimal invariant tests for model discrimination exist when the two models under hypotheses represent scale-regression families. These tests are based on the ratio of the marginal likelihoods of the two families, based on the maximal invariant statistics, in order to eliminate the unknown parameters from the likelihood function. However, even in cases where these functions can in principle be found, it may be difficult to make the calculations required, since the resulting formula is expressed in terms of a multidimensional integral. In this paper a simple approximation to optimal invariant tests based on the Laplace formula is discussed. The main regularity condition required is that the maximum likelihood estimates of the scale and regression parameters exist
A Bayesian adjustment of the modified profile likelihood
No full textWe propose an adjustment of the modified profile likelihood based on a suitable matching prior on the parameter of interest only, i.e. a prior for which there is an agreement between frequentist and Bayesian inference.We show that the proposed modified profile likelihood has several desiderable inferential
properties. Two examples are illustrated
Higher-order Bayesian approximations for pseudo-posterior distributions
No full textThe theory of higher-order asymptotics provides accurate approximations to posterior distributions for a scalar parameter of interest, and to the corresponding tail area, for practical use in Bayesian analysis. The aim of this article is to extend these approximations to pseudo-posterior distributions, e.g., posterior distributions based on a pseudo-likelihood function and a suitable prior, which are proved to be particularly useful when the full likelihood is analytically or computationally infeasible. In particular, from a theoretical point of view, we derive the Laplace approximation for a pseudo-posterior distribution, and for the corresponding tail area, for a scalar parameter of interest, also in the presence of nuisance parameters. From a computational point of view, starting from these higher-order approximations, we discuss the higher-order tail area (HOTA) algorithm useful to approximate marginal posterior distributions, and related quantities. Compared to standard Markov cha..
Bounded estimation in the presence of nuisance parameters
No full textThe aim of this paper is to extend in a natural fashion the results on the treatment of nuisance parameters from the profile likelihood theory to the field of robust statistics. Similarly to what happens when there are no nuisance parameters, the attempt is to derive a bounded estimating function for a parameter of interest in the presence of nuisance parameters. The proposed method is based on a classical truncation argument of the theory of robustness applied to a generalized profile score function. By means of comparative studies, we show that this robust procedure for inference in the presence of a nuisance parameter can be used successfully in a parametric setting
Likelihood asymptotics for the stress-strength model P(X<Y)
No full textA stress-strength model is concerned with the statistical problem of evaluating the reliability parameter R = P(X <Y ), where X and Y are taken to be independent random variables. Classical
likelihood based procedures for inference on R are available, but it is well-known that they can be inaccurate when the sample size is small, in particular in the presence of many unknown parameters. In this paper, we discuss and apply higher-order likelihood based procedures to obtain accurate confidence
intervals for R. The accuracy of the proposed methodology is illustrated by numerical studies
Robust inference in composite transformation models
Full text linkThe aim of this paper is to base robust inference about a shape parameter indexing a composite transformation model on a quasi- prole likelihood ratio test statistic. First, a general procedure is presented in order to construct a bounded prole estimating function for shape parameters. This method is based on a standard truncation argument from the theory of robustness. Hence, a quasi-likelihood test is derived. Numerical studies and applications to real data show that its use reveals extremely powerful, leading to improved inferences with respect to classical robust Wald and score-type test statistics
Recent advances on Bayesian inference for P(X min Y )
Full text linkWe address the statistical problem of evaluating R = P(X < Y ), where X and Y are two independent random variables. Bayesian parametric inference about R, based on the marginal posterior density of R, has been widely discussed under various distributional assumptions on X and Y . This classical approach requires both elicitation of a prior on the complete parameter and numerical integration in order to derive the marginal distribution of R. In this paper, we discuss and apply recent advances in Bayesian inference based on higher-order asymptotics and on pseudo-likelihoods, and related matching priors, which allow to perform accurate inference on the parameter of interest only. The proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals.
The accuracy of the proposed methodology is illustrated both by numerical studies and by real-life data concerning clinical studie
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