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i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p = n Y with probability n-1 with probability/ n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZỸ +(1-Z)n where Z~ Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful.

i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p = n Y with probability n-1 with probability/ n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZỸ +(1-Z)n where Z~ Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p= n { JY with probability n-1 with probability 1 n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZY+(1-Z)n Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful. where Z ~
Transcribed Image Text:i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p= n { JY with probability n-1 with probability 1 n Show that p is consistent but not asymptotically unbiased. Hint: We can write p = ZY+(1-Z)n Bern (¹) and Z is independent of Y. Law of Total Probability may also be helpful. where Z ~
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