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B. Stat. – 302 |
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| Aim of the Course | ||||||||||||||||||
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Students should have enough understanding of the main concepts and algorithms of estimation theory for practical application as well as for their research.
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| Objectives of this Course | ||||||||||||||||||
| ⇒ | Understand all properties of a good estimator with application. | |||||||||||||||||
| ⇒ | Understand various methods of point estimators and their characteristics. | |||||||||||||||||
| ⇒ | Understand interval estimators, confidence intervals and confidence limits. | |||||||||||||||||
| ⇒ | Understand optimality properties of Bayesian estimators. | |||||||||||||||||
| Learning Outcomes of this Course | ||||||||||||||||||
| At the end of the course, the students will be able to | ||||||||||||||||||
| ⇒ | Know to use the appropriate method in any estimation problem. | |||||||||||||||||
| ⇒ | Have ability to apply estimation methods to real life of problems. | |||||||||||||||||
| ⇒ | Know to detect the best estimates. | |||||||||||||||||
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| Course Contents | ||||||||||||||||||
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Point Estimation: Principle of point estimation, Consistency, Unbiasedness, Efficiency, Sufficiency, Asymptotic efficiency, Minimum variance bound estimate, Cramer-Rao lower bound.
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Methods of Point Estimation: Introduction, Estimation methods–moments, maximum likelihood, minimum chi-square, least squares and Bayesian, with their properties, Minimax estimators, Point estimators concerning Bernoulli, binomial, Poisson, geometric, uniform, normal, exponential, gamma, beta and Weibull distributions.
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Robust Estimation: Introduction, Necessity, Robust estimation of location and scale parameters of symmetric distributions, Trimmed and Winsorized means, Linear combination of selected order statistics, M, L and R-estimators.
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Nonparametric Estimation: Basic ideas and methods of nonparametric estimation.
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Interval Estimation: Concepts of central and non-central confidence intervals, Estimation methods – Neyman classical, pivotal quantity, large sample, Bayesian and Fiducial, Confidence intervals for parameters of Bernoulli, binomial, Poisson, geometric, uniform, normal, exponential, gamma, beta and Weibull distributions.
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| Main Books Recommended: | ||||||||||||||||||
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1)
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2)
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Hogg, R. V. and A.T. Craig (2008). Introduction to Mathematical Statistics, 6th ed., Pearson Education, Singapore. [Solution]
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3)
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Mood, A.M., F. A. Graybill and D.C. Boes (1994). Introduction to the theory of Statistics. 5th ed., McGraw–Hill, N.Y. [Solution]
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| References: | ||||||||||||||||||
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4)
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Casella, G., & R. L. Berger (2002). Statistical inference. Pacific Grove, CA: Duxbury.
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5)
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Kendall, M.G. and A. Stuart (2010). Advanced Theory of Statistics, 14th ed., Edward Arnold, N.Y. [Volume 01]
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6)
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Lehmann, E.L. and G. Cassela (1998). Theory of Point estimation, Springer Verlag, NY
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7)
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Rao, C. R. (2009). Linear statistical inference and its applications. John Wiley & Sons.
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