math stat trivial pursuit (sort of)for review (math 30)
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Math Stat Trivial Pursuit (Sort of)For Review (math 30). Colors and Categories. Blue – Basics of Estimation Pink – Properties of Estimators and Methods for Estimation Yellow – Hypothesis Testing Brown – Bayesian Methods Green – Regression - PowerPoint PPT PresentationTRANSCRIPT
MATH STAT TRIVIAL PURSUIT (SORT OF) FOR REVIEW (MATH 30)
COLORS AND CATEGORIES
Blue – Basics of Estimation Pink – Properties of Estimators and Methods
for Estimation Yellow – Hypothesis Testing Brown – Bayesian Methods Green – Regression Orange – Nonparametric Procedures and
Categorical Data Analysis
BLUE 1 Suppose you have an estimator theta-hat,
and you want to know its bias. How is bias computed?
BLUE 2 How is MSE of an estimator computed?
BLUE 3 What is a common unbiased point estimator for a
population mean and what is its standard error?
BLUE 4 What is a common unbiased point estimate
of a difference in two population proportions, and what is its standard error?
BLUE 5 A very important result related to samples
from a normal distribution is that: The sample mean is ____________ distributed. The sample variance, appropriately scaled, is
____________ distributed. The sample mean and sample variance are
____________________.
(Fill-in all three blanks for credit).
BLUE 6 What are the 2 properties of pivot quantities
and what are pivots used for?
BLUE 7 How would you use the asymptotic normal
distribution of many unbiased point estimators to create a confidence interval for their respective parameters?
(You can just give the formula).
Hint: Think of a specific case and generalize.
BLUE 8 How is a t distribution formed?
BLUE 9 How is an F distribution formed?
BLUE 10 How do you form a small-sample confidence
interval for a population mean?
PINK 1 If relative efficiency is computed between
two estimators, it means that both estimators were _______________, and if the numerical value of the relative efficiency is 2, then it means that the _____________ (first or second) estimator is better.
PINK 2 What is the definition of consistency for an
estimator?
Bonus: What concept of convergence is this equivalent to?
PINK 3 For an unbiased estimator, what is the “fast”
way of showing consistency?
Bonus: Do you remember what convergence result this was derived from?
PINK 4 If you have a RS of n observations from a
distribution with unknown parameter theta, and T is sufficient for theta, what does that mean?
PINK 5 What is the result you can use to show
sufficiency without resorting to computing conditional pdfs?
PINK 6 What does the Rao-Blackwell Theorem say?
Bonus: What’s the fast way of finding the quantity RB refers to in the end?
PINK 7 Describe how the method of moments works.
PINK 8 Describe how the method of ML estimation
works.
PINK 9 A main property of MLEs is that they are
_____________, which means that ….
PINK 10 If an estimator is NOT admissible (i.e.
inadmissible), what does that mean?
Give an example of an inadmissible estimator.
YELLOW 1 What is the difference between simple and
composite hypotheses?
YELLOW 2 Describe the relationships between the two
types of error in a hypothesis test, as well as their connection to power.
YELLOW 3 If you have a test statistic, you can use either
a rejection region approach or a p-value approach to determine if the null hypothesis should be rejected. What is the difference in the 2 approaches? (Describe).
YELLOW 4 For the common large sample asymptotically
normal z-tests, what is the rejection region for a 2-tailed test?
Bonus: If the significance level is .05 for this test, what is the range of test statistics where you would NOT reject the null hypothesis (numerical values).
YELLOW 5 How are hypothesis tests and confidence
intervals related?
YELLOW 6 What is the difference between the pooled
and unpooled t-tests for 2 independent samples when considering tests for means?
YELLOW 7 In order to determine which 2-sample t-test
for small sample sizes is appropriate, you might have to run a test to check for equality of _______________, and in order to control your overall significance level, you might have to use a ____________ _____________.
YELLOW 8 What does the Neyman-Pearson Lemma say?
(Get the gist of it, what does it let you find, and how?)
YELLOW 9 How do you determine if a most powerful test
is UMP?
YELLOW 10 How do you construct a likelihood ratio test?
What is the asymptotic distribution related to LRTs?
BROWN 1 What is the major difference between
Frequentist and Bayesian approaches to statistics in terms of how the parameter theta is treated?
BROWN 2 What is the difference between a proper and
improper prior?
What is the difference between an informative and uninformative prior?
BROWN 3 How do you find the posterior density of
theta?
BROWN 4 What are conjugate priors?
Give an example of a conjugate prior.
BROWN 5 How would you find the Bayes estimate of:
theta theta(1-theta)
if you had the posterior density of theta?
BROWN 6 A Bayes estimator is ALWAYS a function of a
_______________ statistic because of the _______________ ________________.
BROWN 7 How is a Bayesian credible interval different
from a Frequentist confidence interval?
BROWN 8 Is it possible for Bayesian and Frequentists
intervals to agree? If yes, how might this happen?
BROWN 9 Bayesian hypothesis testing is performed using
______ ________, which are Bayesian analogues of ________ test procedures, and which can allow you to find evidence in favor of your ___________ hypothesis.
BROWN 10 What are some of the issues related to
working with Bayes’ factors?
GREEN 1 Relationships between two variables, X and Y
can be deterministic or ________________. Regression is used when the relationship is _______________. This means that ….
GREEN 2 When first developing regression models, this
is the only constraint on the error terms.
GREEN 3 If your regression model was:
Then how many parameters do you need to estimate?
3322110)( xxxYE
GREEN 4 In least squares solutions for regression,
what quantity is minimized to find the solution?
(You can just give the simple LR quantity).
GREEN 5 The least squares estimates are all
____________, and their variances are functions of _____________, which in turn can be estimated by _______, which is equal to (1/(n-2))SSE.
GREEN 6 What is the full set of conditions on the error
terms in order to get normal sampling distributions for the parameter estimates if sigma is known?
GREEN 7 Why do we end up using a t distribution for
inference about slope parameters in regression instead of a normal distribution?
GREEN 8 What is the main difference between a
confidence interval for a mean response and a prediction interval for an individual response in regression?
GREEN 9 How are CIs for mean responses and
prediction intervals for individual responses affected as the chosen x moves further from the mean of the x’s?
GREEN 10 What is correlation and how do we test about
it?
ORANGE 1 Describe the two-sample shift model.
ORANGE 2 Describe how the sign test works.
ORANGE 3 Describe how the signed rank test works.
ORANGE 4 Describe how the Wilcoxon Rank Sum/Mann-
Whitney U test works.
ORANGE 5 How does a Kolmogorov-Smirnov one-sample
test work? Is the null hypothesis in the procedure simple or composite?
ORANGE 6 How does the 2-sample Kolmogorov-Smirnov
test work?
ORANGE 7 When performing categorical data analysis,
the main distribution you need to understand for the theoretical setup of problems is the ______________ distribution, but the test statistics turn out to have a different distribution, which is the ________________ distribution.
ORANGE 8 How is a chi-square goodness of fit test
performed? When should you perform one?
ORANGE 9 How (and when) does a chi-square test of
independence work?
ORANGE 10 For 2x2 tables, inference is also possible
with: _________ exact test for small sample sizes _________ ratios, which relies on an asymptotic
______ distribution for it’s natural log.
Takehome Final Exam is due Friday, May 13th at 5 p.m. SHARP.
Office Hours (see front cover of exam): Monday 9-12 during my other course’s exam Tuesday 10-12 Wednesday 1-3 Thursday 1-3 Any other time by appt. – just send me an email!
REMINDER:
Math dept. end of semester picnic is Saturday from 12-2 at the Alumni House
THANKS FOR A GREAT SEMESTER!