University of Rajasthan 2007 M.Sc Statistics M.A./ - university paper

Paper IX: ADVANCED DESIGN OF EXPERIMENTS AND SAMPLE THEORY
3 hrs. duration 100 Marks

Section-A
Linear estimation. Guass Mark off theorem. Testing of hypothesis (involving several linear functions. test of sub-hypothesis and test involving equality of a few of the parameters). Introduction to 1 way random model and estimation of variance components.

General theory of analysis of experimental designs. Designs for 2 way elimination of heterogeneity. Desirable properties of a good Design: Orthogonality, Connectedness and Balance, different Optimality Criteria and their interpretations. Relation ranging from blocks of incomplete block designs, duality, resolvability and affine resolvability. Theorems on bounds.

Group divisible, lattice and linked block designs- intrablock analysis. Latin square and Youden square designs. Combination of outcome in group of experiments

Construction of orthogonal latin squares- (i) for prime power numbers and (ii) by Mann- Mechneish theorem, simple methods of construction of BIB designs. Construction of symmetrical fractional factorial designs.

Section-B
Quenouille's Technique of Bias Reduction and its application to ratio kind estimators. Ratio-method of estimation under Midzune Scheme of Sampling When X is Known.

Multivariate Extension of Ratio and Regrression estimators.

Double Sampling for Ratio and Regression Methods of Estimation

Definition of T-classes. Varying probability sampling with and without replacement. Unbaised estimators of variance of Horvitz and Thompson's estimator. Rao-Hartley and Cochran Sampling Scheme and their estimation procedure.

The theory of Multi-stage Sampling with varying probabilities with or without replacement. problems in small area estimation-Syntheitic and generalized regression estimatotrs.

Non Sampling errors and baised response randomized responses for variables, Errors in surveys, Modelling Observational errors, estimation of variance components, application to longitudinal studies (repetitive surveys).

Variance estimation, method of random groups, balanced half samples (IPNSS), Jack-Knife method.

Introduction to super population models.

Reference:
Atkinson,A.C. and Donev,A.N.:Optimal Experimental Design, Oxford University Press
Rao,C.R. and Kleffe,J.: Estimation of Variance Components and Applications.
Searle,S.R., Casella,G and McCulloch,C.E.: Variance Components, John Wiley, New York.
Raghava Rao: construction and Combinatotial issues in Design of Experiments.
Chaudhary,A. and J.W.E., Vos(1988), Unified theory and strategies of survey Sampling, North Holland Amsterdam.
Hedayat,A.S. and Sinha,B.K.: Design and Inference Infinite population Sampling, Wiley
Chaudhary,A and R.Mukharjee: Randomised Response: Theory and Techniques, New York: Marcel Dekker
Mukhopadhyay,T: Small Area Estimation in Survey Sampling, Narosa
Sukhatme,P.V.,Sukhatme,B.V.,Sukhatme Shashikala and C.Ashok: Sampling Theory of Surveys with Applications

Earning:   Approval pending.