All Material

Question 1

Requirements for a consistent estimator

Answer 1

Asymptotically unbiased and variance goes to 0 as n goes to infinity

Question 2

What is the likelihood ratio test statistic?

Answer 2

2*(Difference in Log-likelihoods)

Question 3

What is the Score statistic?

Answer 3

(Score Matrix Transpose)(Inverse of information matrix)(Score Matrix)

Question 4

What distribution does the Score Statistic Follow?

Answer 4

Chi-square

Question 5

What is the Pearson Residual

Answer 5

Residual divided by standard deviation of Yi

Question 6

What is the Standardized Pearson Residual

Answer 6

Pearson Residual divided by sqrt(1-leverage)

Question 7

Where can you find leverages

Answer 7

The diagonal of the Hat Matrix

Question 8

What is the Hat Matrix?

Answer 8

Matrix that projects the observations to the fitted values. Is a measure of leverage.

Question 9

What type of regression is the Hosmer-Lemeshow statistic used for?

Answer 9

Logistic Regression

Question 10

What is the difference between the Hosmer-Lemeshow and Chi-Square Statistics?

Answer 10

Hosmer-Lemeshow groups data by fitted probabilities instead of by x values

Question 11

What is the cumulative logit function?

Answer 11

Ln(prob in category j or less/prob in category more than j) measures probabilities of responses that have a natural order - ex. 1,2,3,4

Question 12

What is the adjacent category logit function

Answer 12

Ln(prob cat. j/prob cat. j+1) used when response has a natural order

Question 13

How to determine if a Time series is parameter redundant

Answer 13

Rewrite model in terms of B and if both sides have the same factor, it is redundant

Question 14

What are deviance residuals?

Answer 14

The square root of an observation’s contribution to the deviance 2*difference in log-likelihood from saturated model vs fitted model

Question 15

Formula for sample auto covariance

Answer 15

Sum( (x of t+h - sample mean)*(x of t - sample mean))/n

Question 16

How to get variance from information

Answer 16

Variance = 1/information

Question 17

Variance of sample mean

Answer 17

Var (x)/N

Question 18

Method of moments poisson shortcut

Answer 18

Lambda = sample mean

Question 19

Method of moments negative binomial shortcut

Answer 19

Beta = sample mean / r

Question 20

Method of moments Binomial shortcut

Answer 20

q= sample mean / m

Question 21

For which distributions is maximum likelihood the same as method of moments

Answer 21

Exponential, gamma with a fixed, poisson, binomial with m fixed, negative binomial with r fixed, normal

Question 22

Maximum likelihood estimators for uniform distribution

Answer 22

The sample minimum and maximum

Question 23

How do you calculate likelihood when there is a deductible

Answer 23

Divide f(x) by S(d)

Question 24

Pareto trick for maximum likelihood

Answer 24

(number of uncensored values)/sum ln ( theta + x)/(theta + d)

Question 25

Exponential trick for maximum likelihood

Answer 25

Sum of Payments/# of uncensored values

Question 26

What is the kolmogorov-smirnov test

Answer 26

Max difference between empirical dist. At x and fitted dist. At x, across all x's

Question 27

How to tell if a statistic is sufficient

Answer 27

The likelihood function can be writing as a product of a factor containing the statistic and parameter, and a factor not a function of the statistic.

Question 28

How to test the mean using the sample mean when you know the distribution variance

Answer 28

(sample mean - mu)/(theta/sqrt n) is a unit normal

Question 29

What is the standard deviation of the sample mean

Answer 29

distribution mean/n

Question 30

What distribution does a sum of n unit normals follow

Answer 30

chi-square with n degrees of freedom

Question 31

How to test the variance using the sample variance

Answer 31

sample variance * (n-1)/distribution variance is chi-square with n-1 d.f.

Question 32

How to test the mean using the sample mean when you don't know the distribution variance

Answer 32

(sample mean - mu)/(s/sqrt n) has a t-distribution with n d.f.

Question 33

How to test whether two means are the same, samples not paired

Answer 33

Use same rules as if testing one mean, but use a combined normal distribution of the two samples

Question 34

How to test whether two means are the same, samples paired

Answer 34

use the t-distribution where the sample mean and sample variances are from the sample of differences of each pair

Question 35

What is the power of a hypothesis test

Answer 35

Probability that you reject H0 given H1 is true

Question 36

What is the significance of a hypothesis test

Answer 36

Probability that you reject H0 given that H0 is true

Question 37

What is the F distribution

Answer 37

A ratio of two chi-square distributions divided by their degrees of freedom

Question 38

How to test whether two variances are the same

Answer 38

Ratio of sample variances (largest in numerator) has an F distribution with each sample's d.f (n-1)