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

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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
• 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?
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.
Reminder:
• Takehome Final Exam is due Friday, May 13that 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!
Thanks for a Great Semester!
• Math dept. end of semester picnic is Saturday from 12-2 at the Alumni House