For the unbalanced analysis of covariance model with one covariate, a simple formula is given for... more For the unbalanced analysis of covariance model with one covariate, a simple formula is given for the intraclass correlation coefficient estimator that results from Henderson's Method 3 estimation of variance components. Example calculations and the corresponding interpretations are given for a study of the correlation of iron content among brothers. The example illustrates the manner in which the estimator depends
Communications in Statistics - Theory and Methods, 2012
ABSTRACT This article deals with a criterion for selection of variables for the multiple group di... more ABSTRACT This article deals with a criterion for selection of variables for the multiple group discriminant analysis in high-dimensional data. The variable selection models considered for discriminant analysis in Fujikoshi (1985, 2002) are the ones based on additional information due to Rao (1948, 1970). Our criterion is based on Akaike information criterion (AIC) for this model. The AIC has been successfully used in the literature in model selection when the dimension p is smaller than the sample size N. However, the case when p > N has not been considered in the literature, because MLE can not be estimated corresponding to singularity of the within-group covariance matrix. A popular method used to address the singularity problem in high-dimensional classification is the regularized method, which replaces the within-group sample covariance matrix with a ridge-type covariance estimate to stabilize the estimate. In this article, we propose AIC-type criterion by replacing MLE of the within-group covariance matrix with ridge-type estimator. This idea follows Srivastava and Kubokawa (2008). Simulations revealed that our proposed criterion performs well.
ABSTRACT This note examines the effect of equicorrelation of the observations on Grubbs' ... more ABSTRACT This note examines the effect of equicorrelation of the observations on Grubbs' (1950) procedure of detecting an outlier in a sample of n independent observations. It is shown that the procedure is robust, in fact the significance level remains unchanged.
Annals of the Institute of Statistical Mathematics, 1975
Summary It is well known that one-sample orc-sample (location) problems are special cases of the... more Summary It is well known that one-sample orc-sample (location) problems are special cases of the general linear regression modelY i =β1 x 1i +⋯+β k x ki +ε i , where we wish to test the hypothesisH:β1=⋯=β q =0,q⪳. This problem has been considered by Hjek [5] and Srivastava [13], [14], and a class of asymptotically most powerful rank score tests
The asymptotic distributions under local alternatives of two test criteria for testing the hypoth... more The asymptotic distributions under local alternatives of two test criteria for testing the hypothesis that the characteristic roots of the covariance matrix of an elliptical population, assumed distinct, are equal to a set of specified numbers, are derived. The two tests are the ...
The Akaike information criterion (AIC) has been successfully used in the liter- ature in model se... more The Akaike information criterion (AIC) has been successfully used in the liter- ature in model selection when there are a small number of parameters p and a large number of observations N. The cases when p is large and close to N or when p>N have not been considered in the literature. In fact,when p is large and close to
In microarray experiments, the dimension p of the data is very large but there are only few obser... more In microarray experiments, the dimension p of the data is very large but there are only few observations N on the subjects/patients. In this article, the problem of classifying a subject into one of the two groups, when p is large, is considered. Three procedures based on Moore-Penrose inverse of the sample covariance matrix and an empirical Bayes estimate of
For the unbalanced analysis of covariance model with one covariate, a simple formula is given for... more For the unbalanced analysis of covariance model with one covariate, a simple formula is given for the intraclass correlation coefficient estimator that results from Henderson's Method 3 estimation of variance components. Example calculations and the corresponding interpretations are given for a study of the correlation of iron content among brothers. The example illustrates the manner in which the estimator depends
Communications in Statistics - Theory and Methods, 2012
ABSTRACT This article deals with a criterion for selection of variables for the multiple group di... more ABSTRACT This article deals with a criterion for selection of variables for the multiple group discriminant analysis in high-dimensional data. The variable selection models considered for discriminant analysis in Fujikoshi (1985, 2002) are the ones based on additional information due to Rao (1948, 1970). Our criterion is based on Akaike information criterion (AIC) for this model. The AIC has been successfully used in the literature in model selection when the dimension p is smaller than the sample size N. However, the case when p > N has not been considered in the literature, because MLE can not be estimated corresponding to singularity of the within-group covariance matrix. A popular method used to address the singularity problem in high-dimensional classification is the regularized method, which replaces the within-group sample covariance matrix with a ridge-type covariance estimate to stabilize the estimate. In this article, we propose AIC-type criterion by replacing MLE of the within-group covariance matrix with ridge-type estimator. This idea follows Srivastava and Kubokawa (2008). Simulations revealed that our proposed criterion performs well.
ABSTRACT This note examines the effect of equicorrelation of the observations on Grubbs' ... more ABSTRACT This note examines the effect of equicorrelation of the observations on Grubbs' (1950) procedure of detecting an outlier in a sample of n independent observations. It is shown that the procedure is robust, in fact the significance level remains unchanged.
Annals of the Institute of Statistical Mathematics, 1975
Summary It is well known that one-sample orc-sample (location) problems are special cases of the... more Summary It is well known that one-sample orc-sample (location) problems are special cases of the general linear regression modelY i =β1 x 1i +⋯+β k x ki +ε i , where we wish to test the hypothesisH:β1=⋯=β q =0,q⪳. This problem has been considered by Hjek [5] and Srivastava [13], [14], and a class of asymptotically most powerful rank score tests
The asymptotic distributions under local alternatives of two test criteria for testing the hypoth... more The asymptotic distributions under local alternatives of two test criteria for testing the hypothesis that the characteristic roots of the covariance matrix of an elliptical population, assumed distinct, are equal to a set of specified numbers, are derived. The two tests are the ...
The Akaike information criterion (AIC) has been successfully used in the liter- ature in model se... more The Akaike information criterion (AIC) has been successfully used in the liter- ature in model selection when there are a small number of parameters p and a large number of observations N. The cases when p is large and close to N or when p>N have not been considered in the literature. In fact,when p is large and close to
In microarray experiments, the dimension p of the data is very large but there are only few obser... more In microarray experiments, the dimension p of the data is very large but there are only few observations N on the subjects/patients. In this article, the problem of classifying a subject into one of the two groups, when p is large, is considered. Three procedures based on Moore-Penrose inverse of the sample covariance matrix and an empirical Bayes estimate of
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