Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a samp...Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a sample of size n is available from each population. He also extends his ad hoc nuisance parameter removal test to the testing of the equality of two multiple correlation matrices. This paper presents likelihood ratio tests for testing the equality of k multiple correlation coefficients, and also k partial correlation coefficients.展开更多
We propose two variable selection methods in multivariate linear regression with highdimensional covariates.The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predict...We propose two variable selection methods in multivariate linear regression with highdimensional covariates.The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level.The second method extends the univariate forward regression of Wang[(2009).Forward regression for ultra-high dimensional variable screening.Journal of the American Statistical Association,104(488),1512–1524.https://doi.org/10.1198/jasa.2008.tm08516]in a unified way such that the variable selection and model estimation can be obtained simultaneously.We establish the sure screening property for both methods.Simulation and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.展开更多
文摘Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a sample of size n is available from each population. He also extends his ad hoc nuisance parameter removal test to the testing of the equality of two multiple correlation matrices. This paper presents likelihood ratio tests for testing the equality of k multiple correlation coefficients, and also k partial correlation coefficients.
文摘We propose two variable selection methods in multivariate linear regression with highdimensional covariates.The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level.The second method extends the univariate forward regression of Wang[(2009).Forward regression for ultra-high dimensional variable screening.Journal of the American Statistical Association,104(488),1512–1524.https://doi.org/10.1198/jasa.2008.tm08516]in a unified way such that the variable selection and model estimation can be obtained simultaneously.We establish the sure screening property for both methods.Simulation and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.
