**DESCRIPTION OF COURSES**

**AS 605 ADVANCED STATISTICAL INFERENCE (1L+1P) II**

**Object****i****v****e**

This course aims at describing the advanced level topics in statistical methods and statistical inference. This course would prepare students to have a strong base to undertake basic and applied research in Statistics.

**Theory**

UNIT I

Robust estimation and robust tests. Asymptotic techniques, Bayesian inference. Estimation of density function, Conditional inference, Detection and handling of outliers in statistical data.

UNIT II

Loglinear models, saturated models, hierarchical models. Analysis of multi-dimensional contingency tables.

UNIT III

Density Estimation: density estimation in the exploration and presentation of data. Survey of existing methods. Kernel method for univariate data: Rosenblatts naïve estimator, its bias and variance. Consistency of general Kernel estimators, MSE and IMSE. Asymptotic normality of Kernel estimates of density. Estimation of distribution by method of kernels.

UNIT IV

Consistency and asymptotic normality (CAN) of real and vector parameters. Invariance of consistency under continuous transformation. Invariance of CAN estimators under differentiable transformations, generation of CAN estimators using central limit theorem. Exponential class of densities and multinomial distribution. Cramer-Huzurbazar theorem, method of scoring.

**Practicals**

Robust estimation and robust tests. Detection and handling of outliers in statistical data. Conditional inference, Bayesian inference, log-linear models, saturated models and hierarchal models. Estimation of density function. Analysis of multi-dimensional contingency tables.

**Suggested Readings**

- Bishop,Y.M.M., Fienberg, S.E. and Holland, P.W. 1975.
*Discrete Multivariate Analysis: Theory and Practice*. MIT Press, Cambridge. - Casela, G. and Berger, R.L. 2001.
*Statistical Inference*. Duxbury Thompson Learning. - Christensen, R. 1997.
*Log-Linear Models and Logistic Regression*. Springer. - Daniel, W. 1990.
*Applied Nonparametric Statistics*. Houghton Mifflin, Boston. - DeGroot, M.H. 1970.
*Optimal Statistical Decisions*. McGraw Hill. - Efron, B. and Tibshirani, R.J. 1993.
*An Introduction to Bootstrap*. Chapman Hall/CRC. - Ferguson, T.S. 1967.
*Mathematical Statistics, A Decision Theoretical Approach*. Academic Press. - Gibbons, J.D. and Chakraborty, S. 1992.
*Non-Parametric Statistical Inference*. Marcel Dekker. - Gray, H.L. and Schucany, W.R. 1972.
*The Generalized Jackknife Statistics*. Marcel Dekker. - Hogg, R.V. and Craig, A.T. 1999.
*Introduction to Mathematical Statistics.*Prentice Hall. - Kale, B.K. 1999.
*A First Course on Parametric Inference*. Narosa Publication. - Prakasa Rao, B.L.S. 1983.
*Nonparametric Functional Estimation*. Academic Press. - Rao, C.R. 1965.
*Linear Statistical Inference and its Applications*. John Wiley. - Silverman, B.W. 1986.
*Density Estimation for Statistics and Data Analysis*. Chapman and Hall. - Silvey, S.D. 1975.
*Statistical Inference*. Chapman and Hall. - Tapia, R.A. and Thompson, J.R. 1978.
*Nonparametric Probability Density Estimation*. Baltimore: Johns Hopkins University Press. - Tiku, M.L., Tan, W.Y. and Balakrishnan, N. 1986.
*Robust Inference*. Marcel Dekker. - Wald, A. 2004.
*Sequential Analysis*. Dover Publications. - Wasserman, L. 2006.
*All of Nonparametric Statistics.*Springer. - Wetherill, G.B. 1986.
*Regression Analysis with Applications*. Springer.