Test for the mean matrix in a Growth Curve model for high dimensions

Abstract

In this paper, we consider the problem of estimating and testing a general linear hypothesis in a general multivariate linear model, the so called Growth Curve model, when the p × N observation matrix is normally distributed with an unknown covariance matrix.The maximum likelihood estimator (MLE) for the mean is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N . We modify the MLE to an unweighted estimator and propose a new test which we compare with the previous likelihood ratio test (LRT) based on the weighted estimator, i.e., the MLE. We show that the performance of this new test based on the unweighted estimator is better than the LRT based on the MLE.For the high-dimensional case, when p is larger than N , we construct two new tests based on the trace of the variation matrices due to the hypothesis (between sum of squares) and the error (within sum of squares).To compare the performance of all four tests we compute the attained significance level and the empirical power.

Growth curve model for analyzing the effects of Calcium foliar feed on the wilting rate of post-harvest rose flowers

“…Before starting the point for estimating parameters, let us defined two jointly sufficient statistics for estimating parameters in the GCM and their respective distribution as found in Srivastava and Singull (2014). Those statistics are the mean XC (CC ) −1 C and the sum of squares matrix…”

“…It is particularly useful when we have short to moderate time series where one cannot apply standard time series approaches. (Hamid et al(2010), von Rosen andKollo (2005), Srivastava and Singull (2015), Srivastava and Singull (2014), Srivastava and Singull (2017)) have shown that the mean structure for GCM is bilinear, on the contrary, for the ordinary Multivariate Analysis of Variance (MANOVA) model where the mean structure is linear. Since the introduction of GCM by Potthoff and Roy (1964), the model has been extensively explored by several authors including von Rosen and Kollo (2005), Khatri (1966), Rao (1958), Rao (1961), Rao (1966), Rao (1984), von Rosen (2018, for examples.…”