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1454682014-IESISSStatisticsIISyllabusUPSCGuide.pdf (Size: 200.3 KB / Downloads: 4)
STATISTICSII
1. Linear Models Theory of linear estimation. GaussMarkoff setup. Least square
estimators. Use of ginverse. analysis of oneway and two way classified datafixed,
mixed and random effect models. Tests for regression coefficients.
2. Estimation Characteristics of good estimator. Estimation methods of maximum
likelihood, minimum chisquare, moments and least squares. Optimal properties of
maximum likelihood estimators. Minimum variance unbiased estimators. Minimum
variance bound estimators. CramerRao inequality. Bhattacharya bounds. Sufficient
estimator. factorisation theorem. Complete statistics. RaoBlackwell theorem. Confidence
interval estimation. Optimum confidence bounds. Resampling, Bootstrap and Jacknife.
3. Hypotheses testing and Statistical Quality Control
a) Hypothesis testing: Simple and composite hypothesis. Two kinds of error. Critical
region. Different types of critical regions and similar regions. Power function. Most
powerful and uniformly most powerful tests. NeymanPearson fundamental lemma.
Unbiased test. Randomised test. Likelihood ratio test. Wald’s SPRT, OC and ASN
functions. Elements of decision and game theory.
b) Statistical Quality Control: Control Charts for variable and attributes. Acceptance
Sampling by attributesSingle, double, multiple and sequential Sampling plans;
Concepts of AOQL and ATI; Acceptance Sampling by variablesuse of DodgeRomig
and other tables.
4. Multivariate Analysis Multivariate normal distribution. Estimation of mean Vector and
covariance matrix. Distribution of Hotelling’s T2statistic, Mahalanobis’s D2statistic, and
their use in testing. Partial and multiple correlation coefficients in samples from a
multivariate normal population. Wishart’s distribution, its reproductive and other
properties. Wilk’s criterion. Discriminant function. Principal components. Canonical
variates and correlations.