Questions

QBUS6810 (ND) Week 11 Quiz

Multiple choice

Let denote a random sample from a distribution with pdf for , where . Consider a dataset and let the cost function for estimating the model be the negative log-likelihood. Consider the critical point that you found that you found in Question 2 and the formula for the second derivative that you derived in Question 3. What can you conclude? Tick all that apply.

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We are given a question about a random sample from a distribution with a pdf p(y; θ) and a cost function defined as the negative log-likelihood (NLL). The task asks us to evaluate several statements about a critical point found in a prior question and about the second derivative derived earlier, then select all that apply. Since the provided data for answer options is empty in this instance (the answer_options field is an empty list), we cannot definitively confirm which statements hold without additional information. Below is a systematic analysis of each proposed option, along with the kinds of information that would be required to judge them. Option 1: "The critical point is a global minimum of the cost function." - What would be needed: To claim a global minimum, the cost function (NLL) must be convex over the entire parameter domain, or the specific region of interest must be convex and the critical point must lie inside it. If the NLL is convex in θ for all θ i......Login to view full explanation

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