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A test for normality of observations and regression residuals
 Internat. Statist. Rev
, 1987
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you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Fisher Information Test of Normality
, 1998
"... An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on havi ..."
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An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on having the expected Fisher Information under normality based on the sample variance. The test statistic is then constructed as a ratio of the resulting likelihood against that of normality. Since the asymptotic distribution of this test statistic is not available, the critical values for n = 3 to 200 have been obtained by simulation and smoothed using polynomials. An extensive power study shows that the test has superior power against distributions that are symmetric and leptokurtic (longtailed). Another advantage of the test over existing ones is the direct depiction of any deviation from normality in the form of a density estimate. This is evident when the test is applied to several real data sets. Testing of normality in residuals is also investigated. Various approaches in dealing with residuals being possibly heteroscedastic and correlated suffer from a loss of power. The approach with the fewest undesirable features is to use the Ordinary Least
INFORMATION TO USERS
, 1982
"... Niknian, Minoo, "Contributions to the problem of goodnessoffit " (1982). Retrospective Theses and Dissertations. Paper 7469. ..."
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Niknian, Minoo, "Contributions to the problem of goodnessoffit " (1982). Retrospective Theses and Dissertations. Paper 7469.
2.2 The Empirical Likelihood Method........................
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A Robust Rescaled Moment Test for Normality in Regression
"... Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it ..."
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Abstract: Problem statement: Most of the statistical procedures heavily depend on normality assumption of observations. In regression, we assumed that the random disturbances were normally distributed. Since the disturbances were unobserved, normality tests were done on regression residuals. But it is now evident that normality tests on residuals suffer from superimposed normality and often possess very poor power. Approach: This study showed that normality tests suffer huge set back in the presence of outliers. We proposed a new robust omnibus test based on rescaled moments and coefficients of skewness and kurtosis of residuals that we call robust rescaled moment test. Results: Numerical examples and Monte Carlo simulations showed that this proposed test performs better than the existing tests for normality in the presence of outliers. Conclusion/Recommendation: We recommend using our proposed omnibus test instead of the existing tests for checking the normality of the regression residuals.
Department of Economics TESTING FOR NORMALITY IN THE LINEAR REGRESSION MODEL: AN EMPIRICAL LIKELIHOOD RATIO TEST
, 2004
"... The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regression model is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are explored and analyzed using Monte Carlo simulation. The ELR test has good power pro ..."
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The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regression model is derived in this paper. The sampling properties of the ELR test and four other commonly used tests are explored and analyzed using Monte Carlo simulation. The ELR test has good power properties against various alternative hypotheses. Keywords: Regression residual, empirical likelihood ratio, Monte Carlo simulation, normality
1.1 Case Studies: A First Look
"... Diagnostics for normal errors in regression currently utilize ordinary residuals, despite the failure of assumptions validating their use. Case studies here show that such misuse may be critical even in samples of size exceeding currently accepted guidelines. A remedy is to employ recovered errors h ..."
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Diagnostics for normal errors in regression currently utilize ordinary residuals, despite the failure of assumptions validating their use. Case studies here show that such misuse may be critical even in samples of size exceeding currently accepted guidelines. A remedy is to employ recovered errors having the required properties. 1
in Economics at
, 1990
"... In the standard classical regression model the most commonly used procedures for estimation are based on the Ordinary Least Squares Method, which is justified on the basis of well known finitesample properties. However, this model consists of a number of assumptions, such as, for example, homoskeda ..."
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In the standard classical regression model the most commonly used procedures for estimation are based on the Ordinary Least Squares Method, which is justified on the basis of well known finitesample properties. However, this model consists of a number of assumptions, such as, for example, homoskedastic, serially independent and normally distributed disturbances and nonstochastic regressors. By changing these assumptions in one way or another, different estimating situations are created, in many of which the OLS estimator may have no statistical justification at all. Further, alternative estimation methods have often been justified only on the basis of their asymptotic properties, although in practice economists frequently have to base their statistical analysis on a relatively small number of observations. This suggests that the particular estimator to use in any situation
Monte Carlo Analysis in Academic Research
, 2011
"... Monte Carlo analysis is a research strategy that incorporates randomness into the design, implementation or evaluation of theoretical models. It began in the 1940s, when the development of computer hardware and mathematical models made it possible to generate streams of random numbers. These random ..."
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Monte Carlo analysis is a research strategy that incorporates randomness into the design, implementation or evaluation of theoretical models. It began in the 1940s, when the development of computer hardware and mathematical models made it possible to generate streams of random numbers. These random number streams are combined with mathematical models in order to create models and evaluate theories of random processes. This chapter attempts to tame this diverse, unmanageable collection of concepts and methods by dividing simulation projects into three types. The first, commonly called “Monte Carlo simulation,” is used to evaluate statistical estimators. When an estimation procedure is proposed, it is standard procedure to test it against a variety of simulated research problems. A second type of project, referred to as “Markov chain Monte Carlo” (or MCMC), helps researchers to draw conclusions about complicated probability models for which conventional research strategies do not yield insights. The third 1 type of project arises in the study of complex systems, which are characterized by a large number of loosely interconnected, autonomous elements. Commonly known as agentbased models, these simulations have found enthusiastic advocates in environmental and social sciences.