Problem Of Non-normality Research Articles

Sustainability Practices and Financial Profitability: The Case of the World’s Top 20 Crude Palm Oil Producers

Sustainability certifications have been introduced for the palm oil industry to ensure its sustainable operation and the production of highly demanded palm oil. At present, there are several sustainability certifications in the market, namely the Roundtable on Sustainable Palm Oil (RSPO), the Malaysian Sustainable Palm Oil (MSPO), and the Indonesian Sustainable Palm Oil (ISPO) certifications. As the crude palm oil (CPO) becomes the largest product been produced and exported in the palm oil industry, it is assumed that the major CPO producers would adhere to the call for sustainability practices by producing certified palm oil. However, the additional cost of acquiring sustainability certification might hinder them from doing so. Besides, it is unclear on the effect of these certifications on firm profitability since there are very few studies have provided quantitative evidence empirical research focuses specifically on the sustainability certification in palm oil industry context. Thus, this intends to fill this gap by examining the effect of local, that is, MSPO or ISPO and international, that is, RSPO certifications on the financial profitability of the world’s top 20 CPO producers which comprises of the leading global palm oil companies based in Malaysia and Indonesia for the period of 2013 to 2018. General Least Regression is employed due to the problems of non-normality of data, heteroscedasticity, and autocorrelation. The main variable under investigation in this study is RSPO, MSPO, and ISPO, proxied by dummy variable. The results showed no significant difference in profitability of locally certified and non-certified CPO producers. Meanwhile, CPO producers with international certification, that is, RSPO recorded reduced profitability of 5% compared to locally certified producers. Hence, the adverse effect of sustainability certifications calls for intervention from both Malaysian and Indonesian governments as well as palm oil authorities in the respective countries, for example, introduction of tax incentives and/or subsidies to compensate for the reduced profitability and the cost of certification.

Robust Bayesian Approaches in Growth Curve Modeling: Using Student’s t Distributions versus a Semiparametric Method

Despite broad applications of growth curve models, few studies have dealt with a practical issue – nonnormality of data. Previous studies have used Student’s t distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which intraindividual measurement errors follow unknown random distributions with Dirichlet process mixture priors. Based on Monte Carlo simulations, we evaluate the performance of the robust semiparametric Bayesian method and compare it to the robust method using Student’s t distributions as well as the traditional normal-based method. We conclude that the semiparametric Bayesian method is more robust against nonnormal data. An example about the development of mathematical abilities is provided to illustrate the application of robust growth curve modeling, using school children’s Peabody Individual Achievement Test mathematical test scores from the National Longitudinal Survey of Youth 1997 Cohort.

Bayesian Quantile Regression Method to Construct the Low Birth Weight Model

This study aims to implement Bayesian quantile regression method in constructing the model of Low Birth Weight. The data of Low Birth Weight is violated of nonnormal assumption for error terms. This study considers quantile regression approach and use Gibbs sampling algorithm from Bayesian method for fitting the quantile regression model. This study explores the performance of the asymmetric Laplace distribution for working likelihood in posterior estimation process. This study also compare the result of variable selection in quantile regression and Bayesian quantile regression for Low Birth Weight model. This study. proved that Bayesan quantile method produced better model than just quantile approach. Bayesian quantile method proved that it can handle the nonnormal problem although using moderate size of data.

Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

The purposes of this paper is to introduce the ability of the Bayesian quantile regression method in overcoming the problem of the nonnormal errors using asymmetric laplace distribution on simulation study. Method: We generate data and set distribution of error is asymmetric laplace distribution error, which is non normal data. In this research, we solve the nonnormal problem using quantile regression method and Bayesian quantile regression method and then we compare. The approach of the quantile regression is to separate or divide the data into any quantiles, estimate the conditional quantile function and minimize absolute error that is asymmetrical. Bayesian regression method used the asymmetric laplace distribution in likelihood function. Markov Chain Monte Carlo method using Gibbs sampling algorithm is applied then to estimate the parameter in Bayesian regression method. Convergency and confidence interval of parameter estimated are also checked. Result: Bayesian quantile regression method results has more significance parameter and smaller confidence interval than quantile regression method. Conclusion: This study proves that Bayesian quantile regression method can produce acceptable parameter estimate for nonnormal error.

Beyond the Local Mean-Variance Analysis in Continuous Time: The Problem of Non-Normality

The paper investigates the eects of deviations from normality on the estimates of risk premiums and the real equilibrium, short-term interest rate in the conventional rational expectations equilibrium model of Lucas (1978). We consider a time-continuous approach, where both the aggregate consumption process as well as cumulative dividends from risky assets are assumed to be jump-diusion processes. This approach allows for random jumps in the fundamental underlying processes at random time points. Preferences are time separable and additive. We derive testable expressions for these quantities, and confront these with 20. century sample estimates. Since there are non-linear components in the formulas for the risk premiums and the interest rate, we can readily explore what eect deviation from normality has on these quantities. Our results test the boundaries of the conventional model.

Does European high-speed rail affect the current level of air services? An EU-wide analysis

This paper analyses whether the current provision of air services in Europe is impacted by high-speed rail (HSR). An ex-post analysis is carried out considering 161 routes EU-wide using transnational data. We use censored regressions with special attention paid to the presence of outliers in the sample and to the potential problem of non-normality of error terms. It is found that shorter HSR travel times involve less air services, with similar impact on both airline seats and flights. This impact quickly drops between 2.0- and 2.5-h HSR travel time. The impact of HSR frequencies is much more limited. Hubbing strategies led by the airlines have the opposite effect from HSR, as hubs involve more air services. Airline/HSR integration at the airport and cities being served by both central and peripheral stations have no significant impact. Metropolitan and national spatial patterns may help to better understand intermodal effects.

Comparing the performance of modified Ft statistic with ANOVA and Kruskal Wallis test

ANOVA is a classical test statistics for testing the equality of groups. However this test is very sensitive to nonnormality as well as variance heterogeneity. To overcome the problem of nonnormality, robust method such as Ft test statistic can be used but the test statistic can only perform well when the assumption of homoscedasticity is met. This is due to the biasness of mean as a central tendency measure. This study proposed a robust procedure known as modified Ft method which combines the Ft statistics with one of the popular robust scale estimators, MADn, Tn and LMSn. A simulation study was conducted to compare the robustness (Type I error) of the method with respect to its counterpart from the parametric and non parametric aspects, ANOVA and Kruskal Wallis respectively. This innovation enhances the ability of modified Ft statistic to provide good control of Type I error rates. The findings were in favor of the modified Ft method especially for skewed data. The performance of the method was demonstrated on real education data

Indicadores de capacidad aplicados a la deserción en las universidades colombianas

<span>En este trabajo, se presenta una propuesta para implementar los Índices de Capacidad de un Proceso como herramienta para medir la efectividad de un proceso social. Estos índices son ampliamente empleados en la industria de productos de consumo, pero no es clara la forma como pueden ser usados en el control de procesos sociales. El trabajo se centra en el análisis de aquellos procesos que no están normalmente distribuidos y que por lo tanto, en una primera aproximación teórica, no son susceptibles de ser controlados con el uso de Índices de Capacidad. Mediante un doble ejemplo aplicado al caso de la deserción en las universidades colombianas, se ofrece una metodología detallada de cómo solucionar el problema de la no normalidad de los datos con el uso de la transformación de Box-Cox, la distribución de Weibull y el método de percentiles de Clements. De esta manera, se demuestra la aplicabilidad de los métodos y a contrastados en otros ámbitos, a casos concretos de deserción en las universidades colombianas. El método de índices de capacidad puede usarse para evaluar el proceso de deserción y definir las metas reales de deserción, posibles de cumplir. Se propone además, que esta metodología sea usada en el control de otros procesos sociales.</span>

Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA to test for the equality of central tendency measures for two and more than two groups respectively. However, in real life we do not often encounter with this ideal situation. A robust method known as Ft statistic has been identified as an alternative to the above methods in handling the problem of nonnormality. Motivated by the good performance of the method, in this study we proposed to use Ft statistic with three different trimming strategies, namely, i) fixed symmetric trimming (10%, 15% and 20%), ii) fixed asymmetric trimming (10%, 15% and 20%) and iii) empirically determined trimming, to simultaneously handle the problem of nonnormality and heteroscedasticity. To test for the robustness of the procedures towards the violation of the assumptions, several variables were manipulated. The variables are types of distributions and heterogeneity of variances. Type I error for each procedures were then be calculated. This study will be based on simulated data with each procedure been simulated 5000 times. Based on the Type I error rates, we were able to identify which procedures (Ft with different trimming strategies) are robust and have good control of Type I error. The best procedure that should be taken into consideration is the Ft with MOM - Tn for normal distribution, 15% fixed trimming for skewed normal-tailed distribution and MOM - MADn for skewed leptokurtic distribution. This is because, all of the procedures produced the nearest Type I error rates to the nominal level.

Iterative methods for solvingAx=b, GMRES/FOM versus QMR/BiCG

We study the convergence of the GMRES/FOM and QMR/BiCG methods for solving nonsymmetric systems of equationsAx=b. We prove, in exact arithmetic, that any type of residual norm convergence obtained using BiCG can also be obtained using FOM but on a different system of equations. We consider practical comparisons of these procedures when they are applied to the same matrices. We use a unitary invariance shared by both methods, to construct test matrices where we can vary the nonnormality of the test matrix by variations in simplified eigenvector matrices. We used these test problems in two sets of numerical experiments. The first set of experiments was designed to study effects of increasing nonnormality on the convergence of GMRES and QMR. The second set of experiments was designed to track effects of the eigenvalue distribution on the convergence of QMR. In these tests the GMRES residual norms decreased significantly more rapidly than the QMR residual norms but without corresponding decreases in the error norms. Furthermore, as the nonnormality ofA was increased, the GMRES residual norms decreased more rapidly. This led to premature termination of the GMRES procedure on highly nonnormal problems. On the nonnormal test problems the QMR residual norms exhibited less sensitivity to changes in the nonnormality. The convergence of either type of procedure, as measured by the error norms, was delayed by the presence of large or small outliers and affected by the type of eigenvalues, real or complex, in the eigenvalue distribution ofA. For GMRES this effect can be seen only in the error norm plots.

Computerized Brain Tissue Classification of Magnetic Resonance Images: A New Approach to the Problem of Partial Volume Artifact

Due to the finite spatial resolution of digital magnetic resonance images of the brain, and the complexity of anatomical interfaces between brain regions of different tissue type, it is inevitable that some voxels will represent a mixture of two or three different tissue types. Outright assignment of such "bipartial" or "tripartial" voxels to one class or another is more problematic and less reliable than assignment of "full-volume" voxels, wholly representative of a single tissue type. We have developed a computerized system for brain tissue classification of dual echo MR data, which uses a polychotomous logistic model for discriminant analysis, combined with a Bayes allocation rule incorporating differential prior probabilities, and spatial connectivity tests, to assign each voxel in the image to one of four possible classes: gray matter, white matter, cerebrospinal fluid, or unclassified. The system supports automated volumetric analysis of segmented images, has low operational overheads, and compares favorably with previous multivariate or "multispectral" approaches to brain MR image segmentation in terms of both validity (bootstrap misclassification rate = 3.3%) and interoperator reliability (intra-class correlation coefficients for all three tissue classes >0.9). We argue that these improvements in performance stem from better methodological management of the related problems of non-Normality of MR signal intensity values and partial volume artifact.

Comments on using alternatives to normal theory statistics in social and behavioural science.

Some Myths Concerning Parametric and Nonparametric Tests by Hunter and May Hunter and May offer a paper on myths and misconceptions (M and M's) that is an excellent companion article to Brewer (1985), who wrote on M and M's in statistical textbooks. Brewer addressed hypothesis testing, confidence intervals, and sampling distributions and the Central Limit Theorem. Hunter and May extend the M and M motif to parametric and nonparametric statistics, particularly with reference to power, robustness, scale of measurement, the null hypothesis, and generality of application.In the section on power, Hunter and May point out that when underlying assumptions of the parametric test are violated nonparametric tests may be more powerful. They call this a knee - jerk argument because this fact is usually ignored in selecting tests. In considering alternatives to normal theory statistics, they offer what they consider to be the definitive argument: ... the reason some nonparametric tests are less powerful than parametric tests is not because they are nonparametric tests per se, but because they are rank or nominal - scale tests and therefore are based on less information.In contradistinction to their reasoning, consider the following analogy: both an accomplished opera singer sings and an off - key beginning tuba player plays dots and dashes of the International Morse Code. While some may consider the opera singer's notes to be sounds of music, there is, in fact, no more information in those dots and dashes than in the off - key notes of the beginning tuba player, with respect to the code. If the complexity and subtlety of what is often imagined to be included in interval scales is noise and not signal, parametric tests will have no more information available than a rank test, and will be less efficient by trying to discriminate a signal from noise when in fact there isn't any. This is my interpretation of Hemelrijk (1961): the cost of being robust with respect to both Type I and Type II error under nonnormality precludes the t test from remaining the Uniformly Most Powerful Unbiased test under nonnormality.In the M and M section on the robustness of parametric tests, they cite Micceri (1989) as evidence of the widespread problem of nonnormality in psychology and education data. Yet, there are many, many Monte Carlo studies that demonstrate that normal theory tests such as the F and t test are robust to departures from normality. These studies used well known mathematical functions (e.g., cauchy, chi - square, exponetional, uniform) to model real data and showed that so long as sample sizes are about equal, sample sizes are at least 20 - 25 per group, and the tests are two - tailed, rather than one - tailed, the t test is robust.Micceri's (1989) argument, echoed by Hunter and May, was that those mathematical functions are poor models of psychology and education data, and consequently Monte Carlo studies based on them are not convincing. His study pointed out how radical real distributions may be, such as the so - called multi - modal lumpy, extreme bimodal, extreme asymmetric, digit preference, and discrete mass at zero with gap distributions. Nevertheless, a Monte Carlo study by Sawilowsky and Blair (1992) demonstrated by sampling with replacement from Micceri's data sets, that so long as sample sizes were equal, about 20 - 25, and tests were two tailed, the independent and dependent samples t tests were robust by any definition.The real issue of the effects of nonnormality, as indicated by Sawilowsky and Blair (1992), is on the comparative power, not robustness, of the t test. For example, a Monte Carlo comparison (10,000 repetitions) of the power for the t test and Wilcoxon test with a sample size of (5,15) drawn from an extreme asymmetric distribution identified by Micceri (1989) indicated that at the .05 alpha level and effect size of .20Greek not transcribed, the power of the Wilcoxon test was . …

Problems of Nonnormality and Multicollinearity for Forecasting Methods Based on Least Squares

Abstract Many popular forecasting and time-series analysis methods assume that the variable to be forecast can be expressed as a linear function of a set of predictors. The predictors may include variables related in either a correlative or causal fashion to the response variable, lagged values of this variable, or known mathematical functions of time. The method of least squares is used almost exclusively to estimate the parameters in these models. This paper discusses two hazards in the indiscriminant use of least squares; nonnormality of the observations on the variable of interest and multicollinearity among the predictors. Robust estimation methods are suggested as alternatives to least squares for nonnormal data, and a robust version of exponential smoothing is developed. A small Monte Carlo study indicates that the robust procedure can be superior to ordinary exponential smoothing in many situations. The sources and effects of multicollinearity are discussed, and several diagnostic statistics are p...