When analyzing the productivity of rms, one may want to compare how the rms transform a set of inputs x (typically labor, energy or capital) into an output y (typically a quantity of goods produced). The economic eeciency of a rm is then deened in terms of its ability of operating close to or on the production frontier which is the boundary of the production set. The frontier function gives the...

To compute the maximum likelihood estimates the log-likelihood function L is maximized with respect to all model parameters. To check that the maximization has been achieved two things have to be satisfied: 1. The vector of first derivatives with respect to the model parameter L′ should be equal to 0. 2. The negative of the matrix of the second derivatives −L′′ should be a positive definite mat...

When analyzing the productivity of rms one may want to compare how the rms transform a set of inputs x typically labor energy or capital into an output y typically a quantity of goods produced The economic e ciency of a rm is then de ned in terms of its ability of operating close to or on the production frontier which is the boundary of the production set The frontier function gives the maximal...

this article examines statistical inference for  where and are independent but not identically distributed pareto of the first kind (pareto (i)) random variables with same scale parameter but different shape parameters. the maximum likelihood, uniformly minimum variance unbiased and bayes estimators with gamma prior are used for this purpose. simulation studies which compare the estimators are ...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

Inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. In this paper, we derive the Horvitz-Thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. We then introduce an alternative unbiased estimator, corresponding to post-st...

In regression problems over R, the unknown function f often varies more in some coordinates than in others. We show that weighting each coordinate i according to an estimate of the variation of f along coordinate i – e.g. the L1 norm of the ith-directional derivative of f – is an efficient way to significantly improve the performance of distance-based regressors such as kernel and kNN regressor...

Stuetzle and Mittal for ordinary nonparametric kernel regression and Kauermann and Tutz for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators without the need for devices such as second derivative estimation and multiple bandwidths of di erent order We derive a similar estimator in the context of local multivariate es...

We consider the problem of change-point estimation of the instantaneous phase of an observed time series. Such change points, or phase shifts, can be markers of information transfer in complex systems; their analysis occurring in geology, biology and physics, but most notably in neuroscience. We develop two non-parametric approaches to this problem: the cumulative summation (CUSUM) and phase de...

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with respect to the Lp loss. An application to the problem of estimating a signal or its r derivative at a given point is developed and minimax rates are proved to hol...