臺灣博碩士論文加值系統

This thesis is about survey sampling. We take up two areas to study further. One is the problem of post-stratification – the decision to stratify a simple random sample after it is already collected. Another is the application of stratified random sampling for the regression estimation problem. For notation and general concepts, in Chapter 1 we give a short introduction to survey sampling in general and stratified random sampling in particular.
In Chapter 2, we study the problems of poststratification. Why after a simple random sample is collected, we need to stratify the sample for statistical analyses. Some problems arise with poststratification, one is that the sample sizes of different strata are random variables. They have a joint distribution and their moments need to be estimated. We apply the delta method of up to the 5-th order to see if the precision of approximate estimators increase as the order increase. Our conclusion is that it is not necessarily so.
In Chapter 3 we deal with the problem of why and how to apply the stratification method to the regression estimation. In the book Elementary Survey Sampling, 5-th Edition, by Scheaffer, Mendengall lll and Ott (1996), they have an example (but no theory) of applying stratified random sampling to ratio estimation problem. We use similar technique to figure out how to apply the stratification method to the regression problem. An example is provided at the end as demonstration.

Contents
Tables Ⅰ
Illustrations Ⅱ

ABSTRACT 1
Chapter 1 Introduction 2
1.1 Introduction to Sample Survey 2
1.2 Introduction to Simple Random Sampling 3
1.3 Introduction to Stratified Random Sampling 5
1.4 The Purpose of This Thesis 11
Chapter 2 The Poststratification 13
2.1 Introduction to Poststratification 13
2.2 Estimation 18
2.2.1 Estimation of The Population Mean 18
2.2.2 Estimation of Approximate Variance of The Population
Mean Estimator 20
2.3 Example 35
Chapter 3 Regression Estimation in Stratification 39
3.1 Introduction to Regular Regression in Sampling 39
3.2 Regression Estimation in Stratified Random Sampling 46
3.2.1 Separate Regression Estimator 48
3.2.2 Combined Regression Estimator 50
3.3 Example 53
REFERENCES 60

Cochran, William G. (1977). Sampling techniques, 3rd ed, New York: Wiley.

Govindarajulu, Zakkula (1999). Elements of sampling theory and methods, Mexico: Prentice-Hall.

Groves, R.M. (1989). Survey errors and survey costs, New York: Wiley.

Hansen, M.H. and Hurwitz, W.N. and Madow, W.G. (1953). Sample survey methods and theory, Vols. Ⅰand Ⅱ, New York: Wiley.

Holt, D. and Smith, T.M.F. (1979). Post-stratification, Journal of the Royal Statistical Society, Ser. A, No. 142, pp. 33-46.

Jagers, P. and , A. and Trulsson, L. (1985). Post-stratification and ratio estimation: usages of auxiliary information in survey sampling and opinion polls, International
Statistical Review, No. 53, pp. 221-238.

Jessen, Raymond J. (1978). Statistical survey techniques, New York: Wiley.

Kish, L. (1965). Survey sampling, New York: Wiley.

Kish, L. (1995). Methods for design effects, Journal of Official Statistics, No. 11, pp. 55-77.

Levy, Paul S. and Lemeshow, Stanley (1999). Sampling of populations: methods and applications, 3rd ed, New York: Wiley.

Lohr, Sharon L. (1999). Sampling: design and analysis, California: Cole Publishing company.

Scheaffer, Richard L. and Mendenhall, William and Ott, Lyman (1996). Elementary survey sampling, 5th ed, New York: Wadsworth Publishing company, pp. 168-169, pp. 219-222.

Singh, R. and Sukhatme, B.V. (1973). Optimum stratification with ratio and regression methods of estimation, Ann. Inst. Statist. Math., No. 25, pp. 627-633.

Stephan, F.F. (1945). The expected value and variance of the reciprocal and other negative powers of a positive Bernoulli variate, Ann. Math. Stat., No. 16, pp. 50-61.

Thompson, M.E. (1997). Theory of sample surveys, London: Chapman ﹠Hall.

Williams, W.H. (1963). The precision of some unbiased regression estimators, Biometrics,No. 19, pp. 352-361.