Slides_Econ140A_Sample_Mean

Slides_Econ140A_Sample_Mean - 9/28/2011 1 Sample Mean and...

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Unformatted text preview: 9/28/2011 1 Sample Mean and Related Issues Copyright Dick Startz 1 Goals • Make assumptions about data generating process • Derive properties (expectation, variance, distribution) of sample mean. • Hypothesis testing • Confidence intervals Copyright Dick Startz 2 ? ? = ¡ ? + ? , E ? = 0, ? ¢ = + ¢ = ∑? ¢ Copyright Dick Startz 3 Data Generating Process ( DGP ) ? ¢ = + ¢ E() = 0 E(? ¢ ) = E( + ¢ ) = + E( ¢ ) = Copyright Dick Startz 4 Sample mean = 1 ¤ ? ¢ ¥ ¢¦§ ¨ = 2 ? § = + § ? © = + © £ = ? § + ? © 2 Copyright Dick Startz 5 = ? § + ? © 2 = ( + § ) + ( + © ) 2 = + § + © 2 Thm: The sample mean is an unbiased estimator of the expected value. Def: is an unbiased estimator of if E() = . Copyright Dick Startz 6 9/28/2011 2 Proof: Sample mean is unbiased = + 1 + 2 ¡ E = E + 1 + 2 ¡ = + E 1 + E...
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This note was uploaded on 12/26/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.

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Slides_Econ140A_Sample_Mean - 9/28/2011 1 Sample Mean and...

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