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

23 Jan

The desire to predict the complex WSS random process based on the sample by using a linear predictor

is expressed in [1, p. 61 exercise 3.10]. It is asked to chose to minimize the MSE or prediction error power

We are asked to find the optimal prediction parameter and the minimum prediction error power by using the orthogonality principle.

read the conclusion >

(1) |

is expressed in [1, p. 61 exercise 3.10]. It is asked to chose to minimize the MSE or prediction error power

(2) |

We are asked to find the optimal prediction parameter and the minimum prediction error power by using the orthogonality principle.

read the conclusion >

3 Jan

In [1, p. 61 exercise 3.9] we are asked to consider the real linear model

and find the MLE of the slope and the intercept by assuming that is real white Gaussian noise with mean zero and variance . Furthermore it is requested to find the MLE of if in the linear model we set . read the conclusion >

(1) |

and find the MLE of the slope and the intercept by assuming that is real white Gaussian noise with mean zero and variance . Furthermore it is requested to find the MLE of if in the linear model we set . read the conclusion >

22 Sep

In [1, p. 61 exercise 3.8] we are asked to prove that the sample mean is a sufficient statistic for the mean under the conditions of [1, p. 61 exercise 3.4].
Assuming that is known. We are asked to find the MLE of the mean by maximizing .
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25 Apr

In [1, p. 61 exercise 3.7] we are asked to find the MLE of and .
for the conditions of Problem [1, p. 60 exercise 3.4] (see also [2, solution of exercise 3.4]).
We are asked if the MLE of the parameters are asymptotically unbiased , efficient and Gaussianly distributed.

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read the conclusion >

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

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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 >