Question

Suppose the mean (0) boiling point of water is to be estimated. Let X be a single observation of boiling point measured in degrees Celsius. Consider the estimate T(x) - .5.x + .5(100) based on the x-scale. And suppose Y a single observation of boiling point measured in degrees Fahrenheit. Consider the estimate T(y)- .5y+.5(212) based on the y-scale. Note that y (9/5)x +32 Is the estimation process measurennent equivariance? Hint: Verify θ 4-θ

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Answer #1

We hall check whether T(x)=T(y) under y=(9/5)x+32.

Now under y=(9/5)x+32, T(y)=.5*(9x/5+32)+.5*(212)

=9x/10+16+106

=9x/10+122=.9x+122,

which is different from T(y). Hence the process is not estimation equivariant.

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