lecture 4

Question 1

what are the 2 properties of estimators

Answer 1

unbiased: expected value= unknown true value
2. estimator is efficient: has lowest possible variance in the class of estimators under considerations

there will be a tradeoff between bias and efficiency

Question 2

what are the Guass markov assumptions

Answer 2

The error has expected value zero

The errors are serially uncorrelated

The errors have constant variance

The X variable is non-stochastic
(fixed in repeated samples)

Question 3

under markov assumptions what is the best linear unbiased estimator

Answer 3

OLS, lowest vairance in the class

so it the most efficient

Question 4

what is statical inference using an OLS estiamtor

Answer 4

process of using data to make inferences
about unknown population parameters

for example hypothsis tests

Question 5

what do you need to conduct a hypothesis

Answer 5

A hypothesis to be tested (usually described as the null
hypothesis) and an alternative against which it can be tested.

2. A test statistic whose distribution is known under the null
   hypothesis.
3. A decision rule which tells us when to reject the null
   hypothesis and when not to reject it.

Question 6

what is a type 1 error

Answer 6

null hypothesis is true but rejected

Question 7

what is a type 2 error

Answer 7

null hypothesis is false but accepted

Question 8

what is a critical value

Answer 8

a value corresponding to a predetermined
p-value. For example a 5% critical value is a value of the test
statistic which would yield a p-value of 0.05.