# Question: Use Definition 10 5 to show that Y1 the first order

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 parameter of a given distribution if and only if for each c > 0

Definition 10.5

The statistic is a consistent estimator of the parameter of a given distribution if and only if for each c > 0

## Relevant Questions

With reference to Exercise 10.33, use Theorem 10.3 to show that Y1 – 1/n+1 is a consistent estimator of the parameter α. To show that an estimator can be consistent with-out being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first ...If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + · · · + Xn is a sufficient estimator of the parameter θ. Use the results of Theorem 8.1 on page 233 to show that 2 is an asymptotically unbiased estimator of µ2. Use the method of maximum likelihood to rework Exercise 10.58. In exercise Given a random sample of size n from a continuous uniform population, use the method of moments to find formulas for estimating the parameters α and ...Post your question