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

29 Jan

In [1, p. 61 exercise 3.11] it is asked to repeat problem [1, p. 61 exercise 3.10] (see also the solution [2] ) for the general case when the predictor is given as

Furthermore we are asked to show that the optimal prediction coefficients are found by solving [1, p. 157, eq. 6.4 ] and the minimum prediction error power is given by [1, p. 157, eq. 6.5 ]. read the conclusion >

(1) |

Furthermore we are asked to show that the optimal prediction coefficients are found by solving [1, p. 157, eq. 6.4 ] and the minimum prediction error power is given by [1, p. 157, eq. 6.5 ]. read the conclusion >

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 .
read the conclusion >

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.

read the conclusion >

read the conclusion >