Power Function for Inverse Gaussian Regression Models

Woldie, Mammo; Folks, J. Leroy; Chandler, James M.

doi:10.1081/sta-100002257

Cited by 14 publications

(4 citation statements)

References 3 publications

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“…Self et al [22] presented another approach to power calculations based on a noncentral chi-square approximation to the distribution of the likelihood ratio statistic. Woldie et al [26] derived power function for testing hypotheses about the slope in inverse Gaussian models. Lin [14] presented two approaches for estimating local powers of the score test for varying dispersion in exponential family nonlinear models.…”

Section: Alternativesmentioning

confidence: 99%

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

Cao

Lin

2011

Acta Math. Appl. Sin. Engl. Ser.

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The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.

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Section: Alternativesmentioning

confidence: 99%

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

Cao

Lin

2011

Acta Math. Appl. Sin. Engl. Ser.

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“…The power function of the test for the equality of the means of two IG populations is studied by Miura (1978) using Monte Carlo simulation. Woldie et al (2001) investigated the power functions for testing hypotheses about the slope of the inverse Gaussian regression models and obtained the series expressions. However, none of the above considered the monotonicity property.…”

Section: Power Functions Of Tests For Ig Meansmentioning

confidence: 99%

R-Symmetry and the Power Functions of the Tests for Inverse Gaussian Means

Mudholkar

Wang

2009

Communications in Statistics - Theory and Methods

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The two-parameter Inverse Gaussian (IG) distribution is often appropriate for modeling non negative right-skewed data due to the striking similarities with the Gaussian distribution in its basic properties and inference methods. There are about 40 such G-IG analogies developed in literature and were most recently tabulated by Mudholkar and Wang. Of these, the earliest and most commonly noted similarities are the significance tests based on student's t and F distribution for the homogeneity of one, two or several means of the IG populations. However, unlike the corresponding tests in Gaussian theory, little is known about the power function of the basic tests. In this article, we employ the IG-related root-reciprocal IG distribution and a notion of Reciprocal Symmetry to establish the monotonicity of the power function of the test of significance for the IG mean.

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“…Upadhyay et al 26 studied Bayesian analysis methods for the IG as a non-linear regression model. Woldie et al 27 provided IGRM power functions to test the hypothesis of the slope parameter under different conditions. They found that in certain conditions, IGRM produced reliable estimates if the assumption of the normal distribution is violated.…”

Section: Introductionmentioning

confidence: 99%

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

Amin

Faisal

Akram

2021

Journal of Chemometrics

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The influential observation affects the regression model inferences. Literature has shown that the problems of multicollinearity and influential observations can jointly exist in a model. The ridge regression estimator has been developed to handle the challenge of multicollinearity. The detection of influential observations with multicollinearity and its impact on the ridge estimates is necessary for better decision making. In this article, we proposed some influence diagnostics for the inverse Gaussian ridge regression model (IGRRM). The proposed diagnostics are evaluated with the help of a simulation study and two chemometric-related data sets. We found that the covariance ratio (CVR) method is better than other methods for the detection of influential observations under smaller dispersion. While for larger dispersion, all the IGRRM diagnostics perform equally well for the identification of influential observations.

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Power Function for Inverse Gaussian Regression Models

Cited by 14 publications

References 3 publications

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

R-Symmetry and the Power Functions of the Tests for Inverse Gaussian Means

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

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