Consider the likelihood of an i.i.d. sample from a Bernoulli population with parameter 𝑝 𝐿 ( 𝑥 1 , . . . , 𝑥 𝑇 ) = ∏ 𝑡 = 1 𝑇 𝑝 𝑥 𝑡 ( 1 − 𝑝 ) 1 − 𝑥 𝑡 . If you estimate the parameter using a Maximum Likelihood estimator, you obtain the point estimate 𝑝 ̂ = 1 𝑇 ∑ 𝑡 = 1 𝑇 𝑥 𝑡 . The standard error can be computed according to two different approaches as we have seen in class: (1) use the variance-covariance matrix of the score 𝛺 0 ; (2) use the matrix of second derivatives of the standardized log-likelihood 𝐵 0 . What is the formula for the standard error of the estimated parameter, if we follow approach (2)? 单项选择题

A

The standard error of 𝑝 ̂ is 𝕊 𝔼 ( 𝑝 ̂ ) = 1 𝑇 𝑝 ̂ ( 1 − 𝑝 ̂ )

B

The standard error of 𝑝 ̂ is 𝕊 𝔼 ( 𝑝 ̂ ) = 𝑝 ̂ ( 1 − 𝑝 ̂ )

C

The standard error of 𝑝 ̂ is 𝕊 𝔼 ( 𝑝 ̂ ) = 1 𝑇 𝑝 ̂ ( 1 − 𝑝 ̂ )

D

The standard error of 𝑝 ̂ is 𝕊 𝔼 ( 𝑝 ̂ ) = 2 𝑝 ̂ ( 1 − 𝑝 ̂ )

E

There is not enough information to compute the standard error of the estimated parameter.

登录即可查看完整答案

我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

类似问题

Question15 A random variable follows an exponential distribution with parameter [math] if it has the following density: [math] This distribution is often used to model waiting times between events. Imagine you are given i.i.d. data [math] where each [math] is modelled as being drawn from an exponential distribution with parameter [math]. Question: Find the MLE estimate of [math] (select one) (hint: use log-probability) Select one alternative [math] [math] [math] [math] ResetMaximum marks: 3 Flag question undefined

Which one statement is true?

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. 

Which one statement is true?

更多留学生实用工具

加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！