Statistical Inference-I

Introduction

Statistical inference is the process of drawing conclusions about populations or scientific truths from data. There are many modes of performing inference including statistical modeling, data oriented strategies and explicit use of designs and randomization in analyses. A key step in the Statistical Investigation Method is drawing conclusions beyond the observed data. Statisticians often call this “statistical inference. A practitioner can often be left in a debilitating maze of techniques, philosophies and nuance. This course presents the fundamentals of inference in a practical approach for getting things done. The main objective of this course is to provide a strong mathematical and conceptual foundation in the methods of statistical inference, with an emphasis on practical aspects of the interpretation and communication of statistically based conclusions in research. Statistical estimation is concerned with the best estimating a value or range of values for a particular population parameter. It deals with the estimation of parameters, properties of good point estimator and its methods. It also discusses the parameter estimation of different probability distributions and their efficiency. Bayesian Statistics and its comparison with classical estimation approach are part of the content.

Pre-requisities: STAT-401

Textbooks

Hogg, R. M. & Craig, A. T. (2019). Introduction to mathematical statistics. (7th ed.). New York: MacMillan Co.
Mood, A. M., Graybill, F. A. & Boes, D. C. (1997). Introduction to the theory of statistics. London: McGraw Hill.
Lehmann, E. L. (1986). Testing statistical hypotheses. New York: John Wiley & Sons.
Hirai, A. S. (1973). Estimation of statistical parameters. Pakistan: IlmiKhana.
Lindgren, B.W. (1998). Statistical theory. New York: Chapman and Hall.
Stuart, A. & Ord, J. K. (1998). Kendall’s’ advanced theory of statistics (2nd ed.) London: Charles Griffin.

Week	Topics	Book
1	Methods of estimation	Mood & Graybill (Page. 11-25)
2	Method of least squares	Mood & Graybill (Page. 34-41)
3	Method of moments	Hogg & Craig (Page. 66-78)
4	Minimum chi-square	Mood & Graybill (Page. 64-71)
5	Maximum likelihood	Hogg & Craig (Page. 84-91)
6	Bayes method	Hogg & Craig (Page. 94-101)
7	Estimates based on order statistic.	Mood & Graybill (Page. 89-106)
8	Observations, Simultaneous confidence intervals.	Hogg & Craig (Page. 108-119)
9	Properties of a good estimator	Lindgren (Page. 134-148)
10	Efficiency	Lindgren (Page. 150-156)
11	Sufficiency	Lindgren (Page. 160-170)
12	Completeness.	Lindgren (Page. 172-185)
13	Minimum Variance Unbiased estimator.	Lehmann (Page. 188-191)
14	Rao-Black-well Theorem	Lehmann (Page. 198-208)
15	Lehmann sheffe theorem with applications	Lehmann (Page. 210-220)
16	Crammer-Rao Inequality.	Lehmann (Page. 230-248)