This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X Nd. This test is applicable if the sample size, n + 1, and d both go to infinity while d/n ! y 2 (0,1), provided that the limits of tr(k)/d, k = 1, . . . , 8, are finite. The main...

We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional...

I extend the theory on factor models by incorporating local factors into the model. Local factors only affect an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. I derive which factors are...