Unit 2 II Maths stat

The method of maximum likelihood estimates parameters by:

• Minimizing the likelihood function

• Maximizing the likelihood function

• Averaging the data

• Using medians

The likelihood function is based on:

• Sample median

• Sample variance

• Joint probability of observed data

• Interval estimate

MLE of the mean for a normal distribution is:

• Median

• Mode

• Sample mean

• Sample variance

The MLE of variance for normal data is:

• Sample variance without Bessel’s correction

• Mean

• Sum of data

• Zero

Which of the following is "not" a feature of MLE?

• Invariance

• Consistency

• Biasedness in small samples

• Exactness in all samples

The MLE is consistent if:

• Bias increases with sample size

• The estimator converges to the true value

• It always equals the parameter

• It has large variance

The likelihood function depends on:

• Data and parameter

• Sample size only

• Parameter only

• Just the mean

The maximum of a likelihood function occurs where:

• Derivative is maximum

• Second derivative is zero

• Derivative is zero

• Integral equals 1

The MLE method is:

• Based on sample moments

• Based on cumulative distribution

• Irrelevant for large samples

• Based on maximizing likelihood

Method of Moments estimates parameters by:

• Matching moments of population and sample

• Minimizing variance

• Maximizing likelihood

• Sampling distribution