multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors,where single-response analysis and multivariate analysis of variance(...
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multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors,where single-response analysis and multivariate analysis of variance(MANOVA)are two frequently used methods for association ***,both methods have their own *** basis of the former method is independence of multipleresponses and the latter one assumes that multipleresponses are normally *** this work,the authors propose a test statistic for multipleresponse association analysis in high-dimensional situations based on F *** is free of normal distribution assumption and the asymptotic normal distribution is obtained under some regular *** computer simulations and four real data applications show its superiority over single-response analysis and MANOVA methods.
We consider the five classes of multivariate statistical problems identified by James (Ann. Math. Stat. 35 (1964) 475-501), which together cover much of classical multivariate analysis, plus a simpler limiting case, s...
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We consider the five classes of multivariate statistical problems identified by James (Ann. Math. Stat. 35 (1964) 475-501), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of E-1 H where H and E are proportional to high-dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the noncentrality or the covariance parameter of H has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the subcritical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike.
Chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis. In addition to borrowing many techniques from the statistics and engineering literatures, chemometric...
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Chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis. In addition to borrowing many techniques from the statistics and engineering literatures, chemometrics itself has given rise to several new data-analytical methods. This article examines two methods commonly used in chemometrics for predictive modeling-partial least squares and principal components regression-from a statistical perspective. The goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations. These methods include ordinary least squares, variable subset selection, and ridge regression.
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