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Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?

M. Ivette Gomes, Lígia Henriques-Rodrigues (2010)

Discussiones Mathematicae Probability and Statistics

In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying those excesses....

Computational intensive methods for prediction and imputation in time series analysis

Maria Manuela Neves, Clara Cordeiro (2011)

Discussiones Mathematicae Probability and Statistics

One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast...

Computing the distribution of a linear combination of inverted gamma variables

Viktor Witkovský (2001)

Kybernetika

A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized p -values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear...

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...

Directional quantile regression in Octave (and MATLAB)

Pavel Boček, Miroslav Šiman (2016)

Kybernetika

Although many words have been written about two recent directional (regression) quantile concepts, their applications, and the algorithms for computing associated (regression) quantile regions, their software implementation is still not widely available, which, of course, severely hinders the dissemination of both methods. Wanting to partly fill in the gap here, we provide all the codes needed for computing and plotting the multivariate (regression) quantile regions in Octave and MATLAB, describe...

Directional quantile regression in R

Pavel Boček, Miroslav Šiman (2017)

Kybernetika

Recently, the eminently popular standard quantile regression has been generalized to the multiple-output regression setup by means of directional regression quantiles in two rather interrelated ways. Unfortunately, they lead to complicated optimization problems involving parametric programming, and this may be the main obstacle standing in the way of their wide dissemination. The presented R package modQR is intended to address this issue. It originates as a quite faithful translation of the authors'...

Efficiency of cropping system designs via base contrast

U. Bronowicka-Mielniczuk, J. Mielniczuk, T. Przybysz (2000)

Applicationes Mathematicae

The present article is a continuation of previous papers by the same authors devoted to the efficiency of crop rotation experiments. We focus on plans distinguished by the cyclical pattern of the incidence matrix. For practical reasons, we slightly modify the efficiency coefficient. The relation between the resulting efficiency coefficients is examined. In addition, we provide a background material on crop rotation experiments.

Efficient robust estimation of time-series regression models

Pavel Čížek (2008)

Applications of Mathematics

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior...

Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator.

Ana María Pérez-Marín (2008)

SORT

The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guillén, Nielsen and Pérez-Marín, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this...

Estimating the shape parameter of the Topp-Leone distribution based on Type I censored samples

Husam Awni Bayoud (2015)

Applicationes Mathematicae

The shape parameter of the Topp-Leone distribution is estimated from classical and Bayesian points of view based on Type I censored samples. The maximum likelihood and the approximate maximum likelihood estimates are derived. The Bayes estimate and the associated credible interval are approximated by using Lindley's approximation and Markov Chain Monte Carlo using the importance sampling technique. Monte Carlo simulations are performed to compare the performances of the proposed methods. Real and...

Estimation in connecting measurements with constraints of type II

Jaroslav Marek (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is a continuation of the paper [6]. It dealt with parameter estimation in connecting two–stage measurements with constraints of type I. Unlike the paper [6], the current paper is concerned with a model with additional constraints of type II binding parameters of both stages. The article is devoted primarily to the computational aspects of algorithms published in [5] and its aim is to show the power of 𝐇 * -optimum estimators. The aim of the paper is to contribute to a numerical solution...

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