Some Effects of Autocorrelated and Cross-Correlated Noise on the Analysis of Variance,
ARMY ELECTRONICS COMMAND FORT MONMOUTH N J
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The standard estimators of the various means and variances used in the analysis of variance ANOVA hypothesis testing are not suitable if the noise is autocorrelated. For colored noise, the estimates obtained from these standard estimators are biased and their distributions are not the same as the distributions of their white noise counterparts. As a result, hypothesis testing using these estimates is unreliable and misleading. The method of maximum likelihood is used to obtain new estimators of the means and variances required in ANOVA which account for the nonwhite noise effects. These estimators are linear and quadratic forms whose coefficients are derived from the correlation matrix of the noise. Estimates obtained from these new estimators are suitable for use in standard ANOVA hypothesis testing. Some effects of using the wrong estimators in the presence of autocorrelated and cross-correlated noise are investigated, assuming a linear, first-order Markov model for the noise. White noise is a special case of this more general model.
- Statistics and Probability