Mathematical Statistics - 3 Flashcards
Define the observed likelihood function and the log likelihood
l(theta) = log L(theta)

Define the maximum likelihood estimate
The maximum likelihood estimate (theta)hat is the value of theta which maximises L, assuming it exists and is unique
Define the likelihood ratio

Define the generalised likelihood ratio

Define
i) Bias
ii) Mean Square Error
iii) Standard Error



When is a sequence of estimators T1,……, consistent for theta
If Tn converges to theta in probability
Define the normal percentile

Define a confidence interval

Define a pivot
A pivot is a random variable whose distribution doesn’t depend on the statistical parameters
Define the students t(n) distribution

Define the p-value of a test statistic, when should we reject the null hypothesis?
When p-values are small

Define a power function and the conclusions we draw from it
