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Influence diagnostics in exponentiated-Weibull regression models with censored data.

Edwin M. M. Ortega, Vicente G. Cancho, Heleno Bolfarine (2006)

SORT

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from the error assumptions and the presence of outliers and influential observations with the fitted models. The literature provides plenty of approaches for detecting outlying or influential observations in data sets. In this paper, we follow the local influence approach (Cook 1986) in detecting influential observations with exponentiated-Weibull regression models. The relevance of the...

Insensitivity region for variance components in general linear model

Hana Boháčová (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In linear regression models the estimator of variance components needs a suitable choice of a starting point for an iterative procedure for a determination of the estimate. The aim of this paper is to find a criterion for a decision whether a linear regression model enables to determine the estimate reasonably and whether it is possible to do so when using the given data.

Instrumental weighted variables under heteroscedasticity. Part II – Numerical study

Jan Ámos Víšek (2017)

Kybernetika

Results of a numerical study of the behavior of the instrumental weighted variables estimator – in a competition with two other estimators – are presented. The study was performed under various frameworks (homoscedsticity/heteroscedasticity, several level and types of contamination of data, fulfilled/broken orthogonality condition). At the beginning the optimal values of eligible parameters of estimatros in question were empirically established. It was done under the various sizes of data sets and...

Instrumental weighted variables under heteroscedasticity. Part I – Consistency

Jan Ámos Víšek (2017)

Kybernetika

The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also n -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels...

Interval estimation in two way nested unbalanced random model.

R. C. Jain, J. Singh, R. Agrawal (1991)

Trabajos de Estadística

The present paper deals with interval estimation of variance components in two way nested unbalanced random model. Employing a suitable transformation a statistic has been developed and its distribution is well approximated by chi-square. The confidence intervals for variance components and the simultaneous confidence interval for their ratios have been derived.

Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models

Masahiro Inuiguchi, Tetsuzo Tanino (2006)

Kybernetika

In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...

Intrinsic priors for hypothesis testing in normal regression models.

Elías Moreno, F. Javier Girón, Francisco Torres (2003)

RACSAM

Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...

Inversion of 3 × 3 partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters

Karel Hron (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a 3 × 3 partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for 2 × 2 partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation...

Inverting covariance matrices

Czesław Stępniak (2006)

Discussiones Mathematicae Probability and Statistics

Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.

Kolmogorov-Smirnov two-sample test based on regression rank scores

Martin Schindler (2008)

Applications of Mathematics

We derive the two-sample Kolmogorov-Smirnov type test when a nuisance linear regression is present. The test is based on regression rank scores and provides a natural extension of the classical Kolmogorov-Smirnov test. Its asymptotic distributions under the hypothesis and the local alternatives coincide with those of the classical test.

L 1 -penalization in functional linear regression with subgaussian design

Vladimir Koltchinskii, Stanislav Minsker (2014)

Journal de l’École polytechnique — Mathématiques

We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being “sparse” in the sense that it can be represented as a sum of a small number of well separated “spikes”. This can be viewed as an extension of now classical sparse estimation problems to the case of infinite dictionaries. We study an estimator of the regression function...

L 2 -type contraction for systems of conservation laws

Denis Serre, Alexis F. Vasseur (2014)

Journal de l’École polytechnique — Mathématiques

The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in L 1 . However it is not a contraction in L p for any p > 1 . Leger showed in [20] that for a convex flux, it is however a contraction in L 2 up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...

Least squares estimator consistency: a geometric approach

João Tiago Mexia, João Lita da Silva (2006)

Discussiones Mathematicae Probability and Statistics

Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.

Likelihood and parametric heteroscedasticity in normal connected linear models

Joao Tiago Mexia, Pedro Corte Real (2000)

Discussiones Mathematicae Probability and Statistics

A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

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