Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

The beta-Birnbaum-Saunders distribution An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies For the first time based on this distribution the so-called beta-Birnbaum-Saunders distribution is proposed for fatigue life modeling Various properties of the new model including expansions for the moments moment generating function mean deviations density function of the order statistics and their moments are derived We discuss maximum likelihood estimation of the model s parameters The superiority of the new model is illustrated by means of three failure real data sets (C) 2010 Elsevier B V All rights reserved

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data

Flash points (T(FP)) of hydrocarbons are calculated from their flash point numbers, N(FP), with the relationship T(FP) (K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 In turn, the N(FP) values can be predicted from experimental boiling point numbers (Y(BP)) and molecular structure with the equation N(FP) = 0.987 Y(BP) + 0.176D + 0.687T + 0.712B - 0.176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Tellurium tetrachloride: an improved method of preparation

An efficient and practical synthesis of tellurium tetrachloride from elemental tellurium and sulfuryl chloride is described. (C) 2008 Elsevier Ltd. All rights reserved.

An Improved Procedure for the Preparation of [Bis(2,2,2-trifluoroethyl)phosphono]acetic Acid

A different and improved procedure for the preparation of [bis(2,2,2-trifluoroethyl)phosphono]acetic acid in just one step from bis(2,2,2-trifluoroethyl)phosphonate is described. The protocol employs a Michaelis-Becker reaction between commercially available bis(2,2,2-trifluoroethyl) phosphonate and bromoacetic acid, furnishing [bis(2,2,2-trifluoroethyl)phosphono]acetic acid in 50-54% yield.

Improved Road Design for Future Maintenance - Analysis of Road Barrier Repair Costs

The cost of a road construction over its service life is a function of the design, quality of construction, maintenance strategies and maintenance operations. Unfortunately, designers often neglect a very important aspect which is the possibility to perform future maintenance activities. The focus is mainly on other aspects such as investment costs, traffic safety, aesthetic appearance, regional development and environmental effects. This licentiate thesis is a part of a Ph.D. project entitled “Road Design for lower maintenance costs” that aims to examine how the life-cycle costs can be optimized by selection of appropriate geometrical designs for the roads and their components. The result is expected to give a basis for a new method used in the road planning and design process using life-cycle cost analysis with particular emphasis on road maintenance. The project started with a review of literature with the intention to study conditions causing increased needs for road maintenance, the efforts made by the road authorities to satisfy those needs and the improvement potential by consideration of maintenance aspects during planning and design. An investigation was carried out to identify the problems which obstruct due consideration of maintenance aspects during the road planning and design process. This investigation focused mainly on the road planning and design process at the Swedish Road Administration. However, the road planning and design process in Denmark, Finland and Norway were also roughly evaluated to gain a broader knowledge about the research subject. The investigation was carried out in two phases: data collection and data analysis. Data was collected by semi-structured interviews with expert actors involved in planning, design and maintenance and by a review of design-related documents. Data analyses were carried out using a method called “Change Analysis”. This investigation revealed a complex combination of problems which result in inadequate consideration of maintenance aspects. Several urgent needs for changes to eliminate these problems were identified. Another study was carried out to develop a model for calculation of the repair costs for damages of different road barrier types and to analyse how factors such as road type, speed limits, barrier types, barrier placement, type of road section, alignment and seasonal effects affect the barrier damages and the associated repair costs. This study was carried out using a method called the “Case Study Research Method”. Data was collected from 1087 barrier repairs in two regional offices of the Swedish Road Administration, the Central Region and the Western Region. A table was established for both regions containing the repair cost per vehicle kilometre for different combinations of barrier types, road types and speed limits. This table can be used by the designers in the calculation of the life-cycle costs for different road barrier types.