# Question: With reference to Example 9 7 show that if the losses

With reference to Example 9.7, show that if the losses are proportional to the squared errors instead of their absolute values, the risk function becomes

And its minimum is at k = 3/2.

Example 9.7

A random variable has the uniform density

And we want to estimate the parameter θ (the “move” of Nature) on the basis of a single observation. If the decision function is to be of the form d(x) = kx, where k ≥ 1, and the losses are proportional to the absolute value of the errors, that is,

L(kx,θ) = c|kx – θ|

Where c is a positive constant, find the value of k that will minimize the risk.

And its minimum is at k = 3/2.

Example 9.7

A random variable has the uniform density

And we want to estimate the parameter θ (the “move” of Nature) on the basis of a single observation. If the decision function is to be of the form d(x) = kx, where k ≥ 1, and the losses are proportional to the absolute value of the errors, that is,

L(kx,θ) = c|kx – θ|

Where c is a positive constant, find the value of k that will minimize the risk.

## Relevant Questions

A statistician has to decide on the basis of a single observation whether the parameter θ of the density Equals θ1 or θ2, where θ1 < θ2. If he decides on θ1 when the observed value is less than the constant k, on θ2 ...If X1, X2, . . . , Xn constitute a random sample from a population with the mean µ, what condition must be imposed on the constants a1, a2, . . . , an so that a1X1 + a2X2 + · · · + anXn is an unbiased estimator of µ? Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter θ. If X1, X2, and X3 constitute a random sample of size n = 3 from a normal population with the mean µ and the variance σ2, find the efficiency of X1 + 2X2 + X3 / 4 relative to X1 + X2 + X3 / 3 as estimates of µ. Use Definition 10.5 to show that Y1, the first order statistic, is a consistent estimator of the parameter α of a uniform population with β = α + 1. Definition 10.5 The statistic is a consistent estimator of the ...Post your question