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By Krishnaiah P.R., Kanal L.N.

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27) are of the form wj = it follows that the linear discriminant function belongs to the class of linear admissible procedures if the sanfiple spectra are essentially equal to the population spectra. (k) as before. It should be emphasized that smoothing over a band of L frequencies will generally be a good idea when we are interested in estimating population spectra for use in the various discriminant functions. 20) can be replaced by the smoothed versions Mr(k) X~,(k) • , ¢. nj/n, . fjT( •k ) = ( g n j ) l ~, ~ [Xfl( k + k ' ) - Xf.

Repeated measurements on autoregressive processes. J. Amer. Statist. Assoc. 73, 371-378. [8] Anglin, F. M. (1971). Discrimination of earthquakes and explosions using short period seismic array data. Nature 233, 51-52. [9] Azari,R. (1975). Information theoretic properties J s o m e spectral approximations in stationary time series. Dissertation. George Washington University, Washington. [10] Bloomfield, P. (1976). Fourier Analysis of Time Series: An Introduction. Holt, Rinehart and Winston, New York.

Statist. Assoc. 72, 397-402. [13] Box, G. E. P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems. Part I: Effect of inequality of variance in the one-way classification. Ann. Math. Statist. 25, 290-302. 44 R. H. Shumway [14] Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis, Forecasting and Control. Holden-Day, San Francisco. [15] Bricker, P. , Mathews, M. , Tukey, P. , Wachter, K. , and Warner, J. L. (1971). Statistical techniques for talker identification.

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