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On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints

Sandra Donevska, Eva Fišerová, Karel Hron (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches...

On the estimation of the autocorrelation function

Manuel Duarte Ortigueira (2010)

Discussiones Mathematicae Probability and Statistics

The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform...

On the extremal behavior of a Pareto process: an alternative for ARMAX modeling

Marta Ferreira (2012)

Kybernetika

In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order...

On the frequentist and Bayesian approaches to hypothesis testing.

Elías Moreno, F. Javier Girón (2006)

SORT

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...

On the generalization and estimation for the double Poisson distribution.

Mohamed M. Shoukri (1982)

Trabajos de Estadística e Investigación Operativa

The bivariate forms of many important discrete probability distributions have been studied by many statisticians. The trinomial, the double Poisson, the bivariate negative binomial, and the bivariate logarithmic series distributions are in fact the bivariate generalizations of the well known univariate distributions. A systematic account of various families of distributions of bivariate discrete random variables have been given by Patil and Joshi (11), Johnson and Kotz (4), and Mardia (9) in their...

On the outstanding elements and record values in the exponential and gamma populations.

G. S. Lingappaiah (1981)

Trabajos de Estadística e Investigación Operativa

Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution...

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