Partial least squares analysis with cross‐validation for the two‐class problem: A Monte Carlo study

Journal of Chemometrics - Tập 1 Số 3 - Trang 185-196 - 1987
Lars Ståhle1, Svante Wold2
1Department of Pharmacology, Karolinska Institute, Box 60400 S-10401 Stockholm, Sweden
2Research Group for Chemometrics, Institute of Chemistry, University of Umeå, S-90187 Umeå, Sweden

Tóm tắt

AbstractA method for statistical analysis of two independent samples with respect to difference in location is investigated. The method uses the partial least squares projections to latent structures (PLS) with cross‐validation. The relation to classical methods is discussed and a Monte Carlo study is performed to describe how the distribution of the test‐statistic employed depends on the number of objects, the number of variables, the percentage variance explained by the first PLS‐component and the percentage missing values. Polynomial approximations for the dependency of the 50 per cent and the 5 per cent levels of the test‐statistic on these factors are given. The polynomial for the 50 per cent level is complicated, involving several first‐, second‐ and third‐degree terms, whereas the polynomial for the 5 per cent level is dependent only on the number of objects and the size of the first component. A separate Monte Carlo experiment indicates that a moderate difference in sample size does not affect the distribution of the test‐statistic. The multi‐sample location problem is also studied and the effect of increasing the number of samples on the test‐statistic is shown in simulations.

Từ khóa


Tài liệu tham khảo

10.1016/0160-5402(86)90016-1

10.1016/0031-3203(76)90014-5

Carter E. M., 1980, Multivariate Statistical Analysis, 47

10.2307/2348005

Wold H., 1982, Systems Under Indirect Observation, 1

10.1007/BFb0062108

10.1080/01621459.1975.10479865

Stone M., 1974, J. Roy. Statist. Soc. B, 111

10.1080/00401706.1978.10489693

10.1016/B978-0-444-87877-9.50042-X

10.1002/cem.1180010107

R.BergströmandH.WoldFix‐point Estimation in Theory and Practice Vandenhoeck and Ruprecht Göttingen (1983).

Knuth D. E., 1981, Seminumerical Algorithms. Random numbers

10.2307/3001663

Box G. E. P., 1978, Statistics for Experimenters

10.1016/S0003-2670(00)84409-8

10.1016/0091-3057(86)90353-9

Wonnacott T. H., 1977, Introductory Statistics

Miller R. G., 1974, Biometrika, 61, 1

Efron B., 1979, Ann. Stat., 17, 1

Lachenbruch P. A., 1975, Discriminant Analysis

Mardia K. V., 1979, Multivariate Analysis

Thông tin
Thông tin xuất bản

Journal of Chemometrics

Tập 1 Số 3

185-196

Thông tin tác giả