"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

19 Apr

In [1, p. 61 exercise 3.6] we are asked to assume that the variance is to be estimated as well as the mean for the conditions of [1, p. 60 exercise 3.4] (see also [2, solution of exercise 3.4]) . We are asked to prove for the vector parameter , that the Fisher information matrix is

Furthermore we are asked to find the CR bound and to determine if the sample mean is efficient. If additionaly the variance is to be estimated as

then we are asked to determine if this estimator is unbiased and efficient. Hint: We are instructed to use the result that

read the conclusion >

Furthermore we are asked to find the CR bound and to determine if the sample mean is efficient. If additionaly the variance is to be estimated as

then we are asked to determine if this estimator is unbiased and efficient. Hint: We are instructed to use the result that

read the conclusion >

11 Jan

In [1, p. 61 exercise 3.5] we are asked to show that for the conditions of Problem [1, p. 60, exercise 3.4] the CR bound is

and further to give a statement about the efficiency of the sample mean estimator. read the conclusion >

and further to give a statement about the efficiency of the sample mean estimator. read the conclusion >

28 Dez

In [1, p. 60 exercise 3.4] we are asked to prove that the estimate

is an unbiased estimator, given are independent and identically distributed according to a distribution. Furthermore we are asked to also find the variance of the estimator. read the conclusion >

(1) |

is an unbiased estimator, given are independent and identically distributed according to a distribution. Furthermore we are asked to also find the variance of the estimator. read the conclusion >

4 Dez

In [1, p. 60 exercise 3.3] we are asked to prove that the complex multivariate Gaussian PDF reduces to the complex univariate Gaussian PDF if N=1.
read the conclusion >

8 Nov

In [1, p. 60 exercise 3.2] we are asked to proof by using the method of characteristic functions that the sum of squares of N independent and identically distributed N(0,1) random variables has a distribution. read the conclusion >