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Math Stat Trivial Pursuit (Sort of) For Review (math 30)

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)

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  1. Math Stat Trivial Pursuit (Sort of) For Review (math 30)

  2. 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

  3. Blue 1 • Suppose you have an estimator theta-hat, and you want to know its bias. How is bias computed?

  4. Blue 2 • How is MSE of an estimator computed?

  5. Blue 3 • What is a common unbiased point estimator for a population mean and what is its standard error?

  6. Blue 4 • What is a common unbiased point estimate of a difference in two population proportions, and what is its standard error?

  7. 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).

  8. Blue 6 • What are the 2 properties of pivot quantities and what are pivots used for?

  9. 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.

  10. Blue 8 • How is a t distribution formed?

  11. Blue 9 • How is an F distribution formed?

  12. Blue 10 • How do you form a small-sample confidence interval for a population mean?

  13. 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.

  14. Pink 2 • What is the definition of consistency for an estimator? • Bonus: What concept of convergence is this equivalent to?

  15. 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?

  16. 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?

  17. Pink 5 • What is the result you can use to show sufficiency without resorting to computing conditional pdfs?

  18. 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?

  19. Pink 7 • Describe how the method of moments works.

  20. Pink 8 • Describe how the method of ML estimation works.

  21. Pink 9 • A main property of MLEs is that they are _____________, which means that ….

  22. Pink 10 • If an estimator is NOT admissible (i.e. inadmissible), what does that mean? • Give an example of an inadmissible estimator.

  23. Yellow 1 • What is the difference between simple and composite hypotheses?

  24. Yellow 2 • Describe the relationships between the two types of error in a hypothesis test, as well as their connection to power.

  25. 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).

  26. 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).

  27. Yellow 5 • How are hypothesis tests and confidence intervals related?

  28. Yellow 6 • What is the difference between the pooled and unpooled t-tests for 2 independent samples when considering tests for means?

  29. 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 ____________ _____________.

  30. Yellow 8 • What does the Neyman-Pearson Lemma say? • (Get the gist of it, what does it let you find, and how?)

  31. Yellow 9 • How do you determine if a most powerful test is UMP?

  32. Yellow 10 • How do you construct a likelihood ratio test? • What is the asymptotic distribution related to LRTs?

  33. Brown 1 • What is the major difference between Frequentist and Bayesian approaches to statistics in terms of how the parameter theta is treated?

  34. Brown 2 • What is the difference between a proper and improper prior? • What is the difference between an informative and uninformative prior?

  35. Brown 3 • How do you find the posterior density of theta?

  36. Brown 4 • What are conjugate priors? • Give an example of a conjugate prior.

  37. Brown 5 • How would you find the Bayes estimate of: • theta • theta(1-theta) if you had the posterior density of theta?

  38. Brown 6 • A Bayes estimator is ALWAYS a function of a _______________ statistic because of the _______________ ________________.

  39. Brown 7 • How is a Bayesian credible interval different from a Frequentist confidence interval?

  40. Brown 8 • Is it possible for Bayesian and Frequentists intervals to agree? If yes, how might this happen?

  41. 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.

  42. Brown 10 • What are some of the issues related to working with Bayes’ factors?

  43. Green 1 • Relationships between two variables, X and Y can be deterministic or ________________. Regression is used when the relationship is _______________. This means that ….

  44. Green 2 • When first developing regression models, this is the only constraint on the error terms.

  45. Green 3 • If your regression model was: • Then how many parameters do you need to estimate?

  46. Green 4 • In least squares solutions for regression, what quantity is minimized to find the solution? • (You can just give the simple LR quantity).

  47. 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.

  48. 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?

  49. Green 7 • Why do we end up using a t distribution for inference about slope parameters in regression instead of a normal distribution?

  50. 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?

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