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Sampling Distributions and Estimation

In: Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control

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  • Dharmaraja Selvamuthu

    (Indian Institute of Technology Delhi, Department of Mathematics)

  • Dipayan Das

    (Indian Institute of Technology Delhi, Department of Textile Technology)

Abstract

Now, we are ready to discuss the relationship between probability and statistical inference. The two key facts to statistical inference are (a) the population parameters are fixed numbers that are usually unknown and (b) sample statistics are known for any sample. For different samples, we get different values of the statistics and hence this variability is accounted for identifying distributions called sampling distributions. In this chapter, we discuss certain distributions that arise in sampling from normal distribution. The other topics covered in this chapter are as follows: unbiasedness, mean square error, consistency, relative efficiency, sufficiency, minimum variance, Fisher information for a function of a parameter, Cramer–Rao lower bound, efficiency, method of moments, maximum likelihood estimation to find estimators analytically and numerically, and asymptotic distributions of maximum likelihood estimators.

Suggested Citation

  • Dharmaraja Selvamuthu & Dipayan Das, 2018. "Sampling Distributions and Estimation," Springer Books, in: Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control, chapter 0, pages 97-145, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-1736-1_4
    DOI: 10.1007/978-981-13-1736-1_4
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