1,721,138 research outputs found
Bias prevention of maximum likelihood estimates: skew normal and skew t distributions.
Full text linkThe skew normal model is a class of distributions that extends the normal one by including a shape parameter. Despite its nice properties, this model presents some problems with the estimation of the shape parameter. In particular, for moderate sample sizes, the maximum likelihood estimator is infinite with positive probability. In this paper, we use the bias preventive method proposed by First (1993) to estimate the shape parameter. It is proved that this modified maximum likelihood estimator always exists finite. When regression and scale parameters are present, the method is combined with maximum likelihood estimators for these parameters. Finally, also the skew t distribution is considered, which may be viewed as an extension of the skew normal. The same method is applied to this model, considering the degrees of freedom as know
Modified profile likelihoods in models with stratum nuisance parameters
No full textIt is well known, at least through many examples, that when there are many nuisance parameters modified profile likelihoods often perform much better than the profile likeli- hood. Ordinary asymptotics almost totally fail to deal with this issue. For this reason, we study asymptotic properties of the profile and modified profile likelihoods in models for stratified data in a two-index asymptotics setting. This means that both the sample size of the strata, m, and the dimension of the nuisance parameter, q, may increase to infinity. It is shown that in this asymptotic setting modified profile likelihoods give improvements, with respect to the profile likelihood, in terms of consistency of estimators and of asymp- totic distributional properties. In particular, the modified profile likelihood based statistics have the usual asymptotic distribution, provided that 1/m=o(q^−1/3), while the analogous condition for the profile likelihood is 1/m=o(q^−1)
A note on likelihood asymptotics for normal linear regression
No full textHigher-order likelihood methods often give very accurate results. A way to evaluate accuracy is the compaidson of the solutions with the exact ones of the classical theory, when these exist. To this end, we consider inference for a scalar regression parameter in the normal regression setting. In particular, we compare confidence intervals computed from the likelihood and its higher-order modifications with the ones based on the Student t distribution. It is shown that higher-order likelihood methods give accurate approximations to exact results
Integrated likelihoods in parametric survival models for highly clustered censored data
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Integrated likelihoods in survival models with stratum nuisance parameters
No full textWhen inference is about a parameter of interest in presence of many nuisance parameters, in general prole likelihoods perform very poorly and lead to serious bias. For stratied data, this problem is particularly evident in models with stratum nuisance parameters, when the number of strata is relatively high with respect to the within-stratum size. Stratied data are very frequent in many applied settings, such as in cohort studies based on multi-center clinical trials. We consider stratied survival data in a parametric framework under the general assumption of noninformative independent censoring (both type I censoring and random censoring schemes), and for such data an inferential approach based on integrated likelihood is proposed. Appropriately dened integrated likelihoods provide very accurate results in all circumstances. Test statistics based on them provides very accurate inference even in extreme settings. These conclusion were strongly supported by simulation studies. Therefore, the paper suggests to avoid prole likelihood methods and use instead integrated likelihood for inference on highly stratied data with relatively small within-stratum sample sizes
Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions
No full textThe skew normal model is a class of distributions that extends the Gaussian family by including a shape parameter. Despite its nice properties, this model presents some problems with the estimation of the shape parameter. In particular, for moderate sample sizes, the maximum likelihood estimator is infinite with positive probability. As a solution, we use a modified score function as an estimating equation for the shape parameter. It is proved that the resulting modified maximum likelihood estimator is always finite. For confidence intervals a quasi-likelihood approach is considered. When regression and scale parameters are present, the method is combined with maximum likelihood estimators for these parameters. Finally, also the skew t distribution is considered, which may be viewed as an extension of the skew normal. The same method is applied to this model, considering the degrees of freedom as known
Conditional likelihood inference in generalized linear mixed models.
Full text linkConsider a generalized linear model with a canonical link function, containing both fixed and random effects. In this paper, we consider inference about the fixed effects based on a conditional likelihood function. It is shown that this conditional likelihood function is valid for any distribution of the random effects and, hence, the resulting inferences about the fixed effects are insensitive to misspecification of the random effects distribution. Inferences based on the conditional likelihood are compared to those based on the likelihood function of the mixed effects model
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