Determining stratum boundaries with multivariate real data

SUMMARY It is shown that the use of principal component analysis to determine stratum boundaries in multivariate sampling improves estimation of the vector mean. Approximate univariate procedures are applied, utilizing the first principal component as the stratification variate. The proposed method reduces the generalized and total variances, and outperforms the univariate or bivariate procedures for total and linear variances of the mean vector. Examples with real data are analyzed.

[1]  Yasushi Taga,et al.  On optimum stratification for the objective variable based on concomitant variables using prior information , 1967 .

[2]  W. Krzanowski.  Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components , 1987 .

[3]  J. Neyman.  On the Two Different Aspects of the Representative Method: the Method of Stratified Sampling and the Method of Purposive Selection , 1934 .

[4]  Irene Hess,et al.  Stratification: A Practical Investigation , 1966 .

[5]  H. Aoyama,et al.  A study of the stratified random sampling , 1954 .

[6]  Gunnar Ekman.  An Approximation Useful in Univariate Stratification , 1959 .

[7]  OPTIMUM STRATIFICATION WITH TWO CHARACTERS , 1963 .

[8]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis, 2nd Edition. , 1985 .

[9]  A. R. Kokan,et al.  Optimum Allocation in Multivariate Surveys : An Analytical Solution , 1967 .

[10]  Allocation of Sample Size to Strata and Related Problems , 1984 .

[11]  P. Mahalanobis.  On large-scale sample surveys , 1944, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[12]  R. Serfling.  Approximately Optimal Stratification , 1968 .

[13]  Morris H. Hansen,et al.  Sample survey methods and theory , 1955 .

[14]  Optimum stratum boundaries for shellfish surveys , 1985 .

[15]  Samprit Chatterjee.  A study of optimum allocation in multivariate stratified surveys , 1972 .

[16]  Mean Integrated Squared Error Sampling , 1986 .

[17]  K. A. Yeomans,et al.  The Use of Cluster Analysis for Stratification , 1973 .

[18]  Samprit Chatterjee,et al.  Multivariate Stratified Surveys , 1968 .

[19]  On Forming Strata of Equal Aggregate Size , 1964 .

[20]  R. Singh,et al.  Approximately Optimum Stratification on the Auxiliary Variable , 1971 .

[21]  T. Dalenius.  The Problem of Optimum Stratification , 1950 .

[22]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[23]  Leslie Kish,et al.  Multivariate and Multipurpose Stratification , 1978 .

[24]  R. G. Cornell,et al.  Quantifying Gains from Stratification for Optimum and Approximately Optimum Strata Using a Bivariate Normal Model , 1976 .

[25]  K. A. Yeomans,et al.  Further Observations on the Stratification of Birmingham Wards by Clustering: A Riposte , 1975 .

[26]  J. L. Hodges,et al.  Minimum Variance Stratification , 1959 .

[27]  V. K. Sethi,et al.  A NOTE ON OPTIMUM STRATIFICATION OF POPULATIONS FOR ESTIMATING THE POPULATION MEANS , 1963 .

[28]  S. Omule.  Optimum Design in Multivariate Stratified Sampling , 1985 .

[29]  M. Hagood,et al.  Component Indexes as a Basis for Stratification in Sampling , 1945 .

[30]  B. V. Sukhatme,et al.  Optimum stratification in sampling with varying probabilities , 1972 .

[31]  A. Chester,et al.  Optimal allocation in multivariate, two-stage sampling designs , 1987 .

[32]  D. Judkins,et al.  Multivariate stratification with size constraints , 1988 .

[33]  I. Thomsen,et al.  A comparison of approximately optimal stratification given proportional allocation with other methods of stratification and allocation , 1976 .

[34]  George S. Day,et al.  A Supplementary Note on the Use of Cluster Analysis for Stratification , 1975 .

[35]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[36]  J. L. Hodges,et al.  The choice of stratification points , 1957 .