The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Camden Jansen - One of the best experts on this subject based on the ideXlab platform.
-
missmech an r package for testing Homoscedasticity multivariate normality and missing completely at random mcar
Journal of Statistical Software, 2014Co-Authors: Mortaza Jamshidian, Siavash Jalal, Camden JansenAbstract:Researchers are often faced with analyzing data sets that are not complete. To properly analyze such data sets requires the knowledge of the missing data mechanism. If data are missing completely at random (MCAR), then many missing data analysis techniques lead to valid inference. Thus, tests of MCAR are desirable. The package MissMech implements two tests developed by Jamshidian and Jalal (2010) for this purpose. These tests can be run using a function called TestMCARNormality. One of the tests is valid if data are normally distributed, and another test does not require any distributional assumptions for the data. In addition to testing MCAR, in some special cases, the function TestMCARNormality is also able to test whether data have a multivariate normal distribution. As a bonus, the functions in MissMech can also be used for the following additional tasks: (i) test of Homoscedasticity for several groups when data are completely observed, (ii) perform the k-sample test of Anderson-Darling to determine whether k groups of univariate data come from the same distribution, (iii) impute incomplete data sets using two methods, one where normality is assumed and one where no specific distributional assumptions are made, (iv) obtain normal-theory maximum likelihood estimates for mean and covariance matrix when data are incomplete, along with their standard errors, and finally (v) perform the Neyman’s test of uniformity. All of these features are explained in the paper, including examples.
Jean-baptiste Poline - One of the best experts on this subject based on the ideXlab platform.
-
Combined permutation test and mixed-effect model for group average analysis in fMRI.
Human Brain Mapping, 2006Co-Authors: Sébastien Mériaux, Alexis Roche, Ghislaine Dehaene-lambertz, Bertrand Thirion, Jean-baptiste PolineAbstract:In group average analyses, we generalize the classical one-sample t test to account for heterogeneous within-subject uncertainties associated with the estimated effects. Our test statistic is defined as the maximum likelihood ratio corresponding to a Gaussian mixed-effect model. The test's significance level is calibrated using the same sign permutation framework as in Holmes et al., allowing for exact specificity control under a mild symmetry assumption about the subjects' distribution. Because our likelihood ratio test does not rely on Homoscedasticity, it is potentially more sensitive than both the standard t test and its permutation-based version. We present results from the Functional Imaging Analysis Contest 2005 dataset to support this claim.
Thomas Mathew - One of the best experts on this subject based on the ideXlab platform.
-
The simultaneous assessment of normality and Homoscedasticity in linear fixed effects models
Journal of Statistical Theory and Practice, 2017Co-Authors: Ye Yang, Thomas MathewAbstract:This article investigates the problem of simultaneously testing the normality and Homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.
Mortaza Jamshidian - One of the best experts on this subject based on the ideXlab platform.
-
missmech an r package for testing Homoscedasticity multivariate normality and missing completely at random mcar
Journal of Statistical Software, 2014Co-Authors: Mortaza Jamshidian, Siavash Jalal, Camden JansenAbstract:Researchers are often faced with analyzing data sets that are not complete. To properly analyze such data sets requires the knowledge of the missing data mechanism. If data are missing completely at random (MCAR), then many missing data analysis techniques lead to valid inference. Thus, tests of MCAR are desirable. The package MissMech implements two tests developed by Jamshidian and Jalal (2010) for this purpose. These tests can be run using a function called TestMCARNormality. One of the tests is valid if data are normally distributed, and another test does not require any distributional assumptions for the data. In addition to testing MCAR, in some special cases, the function TestMCARNormality is also able to test whether data have a multivariate normal distribution. As a bonus, the functions in MissMech can also be used for the following additional tasks: (i) test of Homoscedasticity for several groups when data are completely observed, (ii) perform the k-sample test of Anderson-Darling to determine whether k groups of univariate data come from the same distribution, (iii) impute incomplete data sets using two methods, one where normality is assumed and one where no specific distributional assumptions are made, (iv) obtain normal-theory maximum likelihood estimates for mean and covariance matrix when data are incomplete, along with their standard errors, and finally (v) perform the Neyman’s test of uniformity. All of these features are explained in the paper, including examples.
-
Tests of Homoscedasticity, normality, and missing completely at random for incomplete multivariate data
Psychometrika, 2010Co-Authors: Mortaza Jamshidian, Siavash JalalAbstract:Test of homogeneity of covariances (or Homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of Homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of MCAR require large sample sizes n and/or large group sample sizes n(i), and they usually fail when applied to non-normal data. Hawkins (1981) proposed a test of multivariate normality and Homoscedasticity that is an exact test for complete data when n(i) are small. This paper proposes a modification of this test for complete data to improve its performance, and extends its application to test of Homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, it is shown that the statistic used in the Hawkins test in conjunction with a nonparametric k-sample test can be used to obtain a nonparametric test of Homoscedasticity that works well for both normal and non-normal data. It is explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for Homoscedasticity, MCAR, and multivariate normality. Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates. Also, a power study of the proposed tests indicates good power. The proposed methods use appropriate missing data imputations to impute missing data. Methods of multiple imputation are described and one of the methods is employed to confirm the result of our single imputation methods. Examples are provided where multiple imputation enables one to identify a group or groups whose covariance matrices differ from the majority of other groups.
Holger Dette - One of the best experts on this subject based on the ideXlab platform.
-
A robust test for Homoscedasticity in nonparametric regression
Journal of Nonparametric Statistics, 2010Co-Authors: Holger Dette, Mareen MarchlewskiAbstract:We consider a nonparametric location scale model and propose a new test for Homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function that vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n −1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some nonrobust tests for a constant scale function, which have recently been proposed in the literature.
-
a test for the parametric form of the variance function in a partial linear regression model
Journal of Statistical Planning and Inference, 2008Co-Authors: Holger Dette, Mareen MarchlewskiAbstract:Abstract We consider the problem of testing for a parametric form of the variance function in a partial linear regression model. A new test is derived, which can detect local alternatives converging to the null hypothesis at a rate n - 1 / 2 and is based on a stochastic process of the integrated variance function. We establish weak convergence to a Gaussian process under the null hypothesis, fixed and local alternatives. In the special case of testing for Homoscedasticity the limiting process is a scaled Brownian bridge. We also compare the finite sample properties with a test based on an L 2 -distance, which was recently proposed by You and Chen [2005. Testing heteroscedasticity in partially linear regression models. Statist. Probab. Lett. 73, 61–70].
-
a simple test for the parametric form of the variance function in nonparametric regression
2006Co-Authors: Holger Dette, Benjamin HetzlerAbstract:In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak smoothness assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to a Gaussian process can be established. In the special case of testing for Homoscedasticity the limiting process is essentially a Brownian bridge, such that critical values are easily available. The new procedure has three main advantages. First, in contrast to many other methods proposed in the literature, it does not depend directly on a smoothing parameter. Secondly, it can detect local alternatives converging to the null hypothesis at a rate n-?=2: Thirdly, in contrast to most of the currently available tests, it does not require strong smoothness assumptions regarding the regression and variance function. We also present a simulation study and compare the tests with the procedures that are currently available for this problem and require the same minimal assumptions.
-
a consistent test for heteroscedasticity in nonparametric regression based on the kernel method
Journal of Statistical Planning and Inference, 2002Co-Authors: Holger DetteAbstract:This paper presents a new residual based test for heteroscedasticity in nonparametric regression. The construction of the test statistic is motivated by the idea that the problem of testing heteroscedasticity is equivalent to the problem of testing pseudoresiduals for a constant mean. Asymptotic normality is established with different rates corresponding to the null hypothesis of Homoscedasticity and the alternative. A Monte Carlo simulation is conducted in order to investigate the finite sample performance of a bootstrap version of the proposed test.