In this paper we consider an extension of the beta regression model proposed
by Ferrari and Cribari-Neto (2004). We extend their model in two different
ways, first, we let the regression structure be nonlinear, second, we allow a
regression structure for the precision parameter, moreover, this regression
structure may also be nonlinear. Generally, the beta regression is useful to
situations where the response is restricted to the standard unit interval and
the regression structure involves regressors and unknown parameters. We derive
general formulae for second-order biases of the maximum likelihood estimators
and use them to define bias-corrected estimators. Our formulae generalizes the
results obtained by Ospina et al. (2006), and are easily implemented by means
of supplementary weighted linear regressions. We also compare these
bias-corrected estimators with three different estimators which are also
bias-free to the second-order, one analytical and the other two based on
bootstrap methods. These estimators are compared by simulation. We present an
empirical application
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the "sensitivities" of processes, namely derivatives of martingale components and a weak notion of infinitesimal generators, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating martingales. The theory comes with convergence results that allow to interpret a large class of Wiener functionals beyond semimartingales as limiting objects of differential forms which can be computed path wisely over finite-dimensional spaces. The theory reveals that solutions of BSDEs are minimizers of energy functionals w.r.t Brownian motion driving noise.MSC 2010 subject classifications: Primary 60H07; secondary 60H25
Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they do not investigated its moments and the order statistics. In this paper the BF density function and the density function of the order statistics are expressed as linear combinations of Fréchet density functions. This is important to obtain some mathematical properties of the BF distribution in terms of the corresponding properties of the Fréchet distribution. We derive explicit expansions for the ordinary moments and L-moments and obtain the order statistics and their moments. We also discuss maximum likelihood estimation and calculate the information matrix which was not known. The information matrix is easily numerically determined. Two applications to real data sets are given to illustrate the potentiality of this distribution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.