# slide3 - Standard error Standard error ^ = V ^ ^ ^ ^,s se...

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1 Standard error ! Standard error ! Estimated standard error ,s , ) ˆ ( V ˆ Θ = σ Θ Θ σ ˆ ˆ ) ˆ ( se Θ n X σ = σ n S ˆ X = σ Θ ˆ 2 Example 1 ! While measuring the thermal conductivity of Armco iron, using a temperature of 100F and a power of 550W, the following 10 measurement of thermal conductivity ( in Btr/hr-ft-F) were obtained: 41.60 41.48 42.34 41.95 41.86 42.18 41.72 42.26 41.81 42.04 ! Find point estimate of the mean conductivity and the estimated standard error.

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Mean square error ! Definition: ! Relative efficiency 2 ) ˆ ( E ) ˆ ( MSE θ Θ = Θ 2 2 2 ) bias ( ) ˆ ( V )] ˆ ( E [ )] ˆ ( E ˆ [ E ) ˆ ( MSE + Θ = Θ θ + Θ Θ = Θ ) ˆ ( MSE ) ˆ ( MSE 2 1 Θ Θ 4 Maximum Likelihood Estimation ! The Maximum Likelihood Estimate , of a parameter θ is the numerical value of θ for which the observed results in the data at hand would have the highest probability of arising. θ
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slide3 - Standard error Standard error ^ = V ^ ^ ^ ^,s se...

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