I came to know from somewhere that there is a technique called delta method which can be used to approximate the distribution of a function of a random variable using the distribution of the random variable itself and the first two moments of the function. It is often used in situations where the distribution of the function is difficult to derive directly, but the distribution of the random variable is known. Can someone kindly refer me to some links\books wherein this method is discussed?
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3$\begingroup$ Wikipedia discusses it, with references and further reading $\endgroup$Henry– Henry2023-07-25 13:47:52 +00:00Commented Jul 25, 2023 at 13:47
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2$\begingroup$ Almost any advanced textbook that covers MLE or asymptotics will provide extensive details and examples. $\endgroup$whuber– whuber ♦2023-07-25 14:27:41 +00:00Commented Jul 25, 2023 at 14:27
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$\begingroup$ Could you kindly tell me one such book of your choice $\endgroup$AgnostMystic– AgnostMystic2023-07-25 16:36:37 +00:00Commented Jul 25, 2023 at 16:36
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2$\begingroup$ Look down at the bottom of the Wikipedia page for some references. $\endgroup$jbowman– jbowman2023-07-26 03:25:15 +00:00Commented Jul 26, 2023 at 3:25
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5$\begingroup$ If you were to walk around stats departments and grab random people in the hallway, a lot of them would probably tell you to check out Casella Berger (mybiostats.files.wordpress.com/2015/03/casella-berger.pdf), specifically 5.5.4/page 240. $\endgroup$Nathan Wycoff– Nathan Wycoff2023-07-31 17:21:04 +00:00Commented Jul 31, 2023 at 17:21
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George Casella and Roger L. Berger wrote the standard textbook for first-year statistical theory in graduate school: Statistical Inference. Their book covers the delta method.