Inference on covariance matrices under rank restrictions

Anderson, 1963, Asymptotic theory for principal component analysis, Ann. Math. Statist., 34, 122, 10.1214/aoms/1177704248 Anderson, 1984 Boik, 1986, Testing the rank of a matrix with applications to the analysis of interactions in ANOVA, J. Amer. Statist. Assoc., 81, 243, 10.1080/01621459.1986.10478267 Boik, 1989, Reduced-rank models for interaction in unequally replicated two-way classifications, J. Multivariate Anal., 28, 69, 10.1016/0047-259X(89)90098-5 Box, 1958, A note on generation of normal deviates, Ann. Math. Statist., 29, 610, 10.1214/aoms/1177706645 Carter, 1980, Asymptotic distribution of the latent roots of the noncentral Wishart distribution and the power of the likelihood ratio test for nonadditivity, Canad. J. Statist., 8, 119, 10.2307/3314677 Carter, 1983, Asymptotic non-null distribution for the locally most powerful invariant test for sphericity, Comm. Statist. A, 12, 1719, 10.1080/03610928308828564 Collings, 1987, Compound random number generators, J. Amer. Statist. Assoc., 82, 525, 10.1080/01621459.1987.10478457 Corsten, 1972, Multiplicative effects in two-way analysis of variance, Statist. Neerlandica, 26, 61, 10.1111/j.1467-9574.1972.tb00173.x Davies, 1982, Procedures for reduced-rank regression, Appl. Statist., 31, 244, 10.2307/2347998 Davis, 1972, On the ratios of the individual latent roots to the trace of a Wishart matrix, J. Multivariate Anal., 2, 440, 10.1016/0047-259X(72)90037-1 Farmer, 1987 Geisser, 1958, An extension of Box's results on the use of the F-distribution in multivariate analysis, Ann. Math. Statist., 29, 885, 10.1214/aoms/1177706545 Grieve, 1984, Tests of sphericity of normal distributions and the analysis of repeated measures designs, Psychometrika, 49, 257, 10.1007/BF02294176 John, 1971, Some optimal multivariate tests, Biometrika, 58, 123 John, 1972, The distribution of a statistic used for testing sphericity of normal distributions, Biometrika, 59, 169, 10.1093/biomet/59.1.169 John, 1976, Fitting sampling distribution agreeing in support and moments and tables of critical values of sphericity criterion, J. Multivariate Anal., 6, 601, 10.1016/0047-259X(76)90007-5 Johnson, 1972, An analysis of a two-way model with interaction and no replication, J. Amer. Statist. Assoc., 67, 862, 10.1080/01621459.1972.10481307 Krishnaiah, 1971, On the exact distributions of extreme roots of the Wishart and MANOVA matrices, J. Multivariate Anal., 1, 108, 10.1016/0047-259X(71)90032-7 Krishnaiah, 1972, On the exact distribution of the traces of S1(S1 + S2)−1 and S1S2−1, Sankhya Ser. A, 34, 153 Krzanowski, 1979, Some exact percentage points of a statistic useful in analysis of variance and principal component analysis, Technometrics, 21, 261, 10.1080/00401706.1979.10489759 Lam, 1987, Confidence limits for noncentrality parameters of noncentral chi-squared and F distributions, 441 Mandel, 1961, Non-additivity in two-way analysis of variance, J. Amer. Statist. Assoc., 56, 878, 10.1080/01621459.1961.10482132 Mandel, 1971, A new analysis of variance model for non-additivity, Technometrics, 13, 1, 10.1080/00401706.1971.10488751 Marasinghe, 1985, Asymptotic tests and Monte Carlo studies associated with the multiplicative interaction model, Comm. Statist. A, 11, 2219, 10.1080/03610928508829039 Muirhead, 1982 Nagao, 1973, On some test criteria for covariance matrix, Ann. Statist., 1, 700, 10.1214/aos/1176342464 Schott, 1984, Optimal bounds for the distributions of some test criteria for tests of dimensionality, Biometrika, 71, 561, 10.1093/biomet/71.3.561 Schott, 1986, A note on the critical values used in stepwise tests for multiplicative components of interaction, Comm. Statist. A, 15, 1561, 10.1080/03610928608829202 Schuurmann, 1973, On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix, J. Multivariate Anal., 3, 445, 10.1016/0047-259X(73)90033-X Schuurmann, 1973, Tables for the distributions of the ratios of the extreme roots to the trace of Wishart matrix, Aerospace Research Laboratories Technical Report No. 73-0010 Siotani, 1985 Sugiura, 1972, Locally best invariant test for sphericity and the limiting distributions, Ann. Math. Statist., 43, 1312, 10.1214/aoms/1177692481 Tso, 1981, Reduced-rank regression and canonical analysis, J. Roy. Statist. Soc. B, 43, 183 Williams, 1962, A confidence interval for variance components, Biometrika, 49, 278, 10.1093/biomet/49.1-2.278 Yochmowitz, 1978, Stepwise tests for multiplicative components of interaction, Technometrics, 20, 79, 10.1080/00401706.1978.10489619 Zerbe, 1979, Randomization analysis of the completely randomized design extended to growth and response curves, J. Amer. Statist. Assoc., 74, 215, 10.1080/01621459.1979.10481640