Suppose that X1,X2,...,Xn and Y1,Y2,...,Yn denote independent random samples from populations...
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Suppose that {eq}X1,X2,...,Xn {/eq} and {eq}Y1,Y2,...,Yn {/eq} denote independent random samples from populations with means {eq}\mu_x {/eq} and {eq}\mu_y {/eq} and variances {eq}\sigma^2_x {/eq} and {eq}\sigma^2_y {/eq} respectively.
Show that {eq}\bar{X} - \bar{Y} {/eq} is a consistent estimator of {eq}\mu_x - \mu_y {/eq}
Unbiased Estimator
An unbiased estimator may or may not be a consistent estimator of the population parameter. On the contrary, a biased estimator can also be a consistent estimator. The comparison between a biased and an unbiased estimator is done through the mean square error.
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{eq}{X_1},{X_2},...,{X_n}{/eq} and {eq}{Y_1},{Y_2},...,{Y_n}{/eq} are an independent random sample from populations with mean...
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Biased vs. Unbiased Estimator | Definition, Examples & Statistics
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Chapter 9 / Lesson 7
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Study the difference between the biased estimator and the unbiased estimator. Learn what the terms "unbiased statistics" and "unbiased sample" indicate.
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