2006, Vol. 30, Núm. 1
http://hdl.handle.net/2099/3783
2024-03-28T20:28:12ZOn the frequentist and Bayesian approaches to hypothesis testing.
http://hdl.handle.net/2099/3789
On the frequentist and Bayesian approaches to hypothesis testing.
Girón González-Torre, Francisco Javier; Moreno, Elías
Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given.
2007-11-15T17:55:03ZGirón González-Torre, Francisco JavierMoreno, ElíasHypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given.The importance of being the upper bound in the bivariate family.
http://hdl.handle.net/2099/3788
The importance of being the upper bound in the bivariate family.
Cuadras, C.M. (Carlos Maria)
Any bivariate cdf is bounded by the Fr ´echet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit
assesment. Any random variable can be expanded in terms of some functions related to this bound.The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is
equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound.
2007-11-15T17:51:12ZCuadras, C.M. (Carlos Maria)Any bivariate cdf is bounded by the Fr ´echet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit
assesment. Any random variable can be expanded in terms of some functions related to this bound.The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is
equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound.A matrix function useful in the estimation of linear continuous-time models.
http://hdl.handle.net/2099/3787
A matrix function useful in the estimation of linear continuous-time models.
Neudecker, Heinz
In a recent publication Chen & Zadrozny (2001) derive some equations for efficiently computing eA and ∇ eA, its derivative. They employ an expression due to Bellman (1960), Snider (1964) and Wilcox (1967) for the differential deA and a method due to Van Loan (1978) to find the derivative ∇eA. The
present note gives a) a short derivation of ∇ eA by way of the Bellman-Snider-Wilcox result, b) a shorter derivation without using it. In both approaches there is no need for Van Loan’s method.
2007-11-15T17:46:19ZNeudecker, HeinzIn a recent publication Chen & Zadrozny (2001) derive some equations for efficiently computing eA and ∇ eA, its derivative. They employ an expression due to Bellman (1960), Snider (1964) and Wilcox (1967) for the differential deA and a method due to Van Loan (1978) to find the derivative ∇eA. The
present note gives a) a short derivation of ∇ eA by way of the Bellman-Snider-Wilcox result, b) a shorter derivation without using it. In both approaches there is no need for Van Loan’s method.About one problem of Bernoulli and Euler from the theory of statistical estimation.
http://hdl.handle.net/2099/3786
About one problem of Bernoulli and Euler from the theory of statistical estimation.
Nikulin, Mikhaïl
We consider some results by D. Bernoulli and L. Euler on the method of maximum likelihood in parametric estimation. The statistical analysis is made by considering a parametric family with a shift parameter.
2007-11-15T17:42:10ZNikulin, MikhaïlWe consider some results by D. Bernoulli and L. Euler on the method of maximum likelihood in parametric estimation. The statistical analysis is made by considering a parametric family with a shift parameter.Improving small area estimation by combining surveys: new perspectives in regional statistics.
http://hdl.handle.net/2099/3785
Improving small area estimation by combining surveys: new perspectives in regional statistics.
Costa, Àlex; Satorra, A.; Ventura, Eva
A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a
complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.
2007-11-15T16:59:50ZCosta, ÀlexSatorra, A.Ventura, EvaA national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a
complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.