(Requires Appendix Material and Calculus)The Logarithm of the Likelihood Function $\frac { n } { 2 }$

question 42

Essay

(Requires Appendix material and Calculus)The logarithm of the likelihood function (L)for estimating the population mean and variance for an i.i.d. normal sample is as follows (note that taking the logarithm of the likelihood function simplifies maximization. It is a monotonic transformation of the likelihood function, meaning that this transformation does not affect the choice of maximum):
L = - $\frac { n } { 2 }$ log(2πσ²)- $\frac { 1 } { 2 \sigma ^ { 2 } } \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \mu _ { Y } \right) ^ { 2 }$ Derive the maximum likelihood estimator for the mean and the variance. How do they differ, if at all, from the OLS estimator? Given that the OLS estimators are unbiased, what can you say about the maximum likelihood estimators here? Is the estimator for the variance consistent?

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Definitions:

Encoding

The process of converting information or data into a particular form, especially within the context of communication or data processing.

Decoding

The process of interpreting or understanding information, symbols, or messages in communication.

Perception

The process by which individuals interpret and organize sensory information to make meaningful interpretations of the world.

Lengel-Daft Contingency Model

is a theoretical framework suggesting that the effectiveness of communication in organizations depends on the alignment between the information processing needs and the capacity of the information system.