MT427 Mathematical Statistics

Spring 2011

Prof. Dan Chambers

Office: 365 Carney

chambers@bc.edu

617-552-3769 (email is more reliable)

Office Hours: Mondays 12-1, Wednesdays 9-10, Fridays 3-4, or by appointment.

The text we'll use is An Introduction to Mathematical Statistics and Its Applications, 4th Edition, by Richard Larsen and Morris Marx. We'll finish chapter 4, then cover chapters 5-7, 9, 10, and some of 14.

Spring 2011

Prof. Dan Chambers

Office: 365 Carney

chambers@bc.edu

617-552-3769 (email is more reliable)

Mathematical
Statistics is a
continuation of MT426 Probability or an equivalent (calculus-based)
probability course. Whereas probability takes a given distribution and
calculates the probability of seeing certain data values, statistics
takes data and attempts to find the distribution that generates it,
estimate parameters of the underlying distribution, and test hypotheses
about those parameters.

Some of the topics we'll be covering this semester are: the central limit theorem, maximum likelihood estimation, method of moments estimation, confidence intervals, minimum-variance estimators, Cramer-Rao lower bound, sufficiency and consistency of estimators, hypothesis testing: binomial parameter, t test, Z test, generalized likelihood ratio, inferences about variances, two sample problems, goodness-of-fit tests, tests of independence and homogeneity, and nonparametric statistics.

Here is a link to the syllabus.

Here is a review of probability and some of the important distributions and their properties.

Some of the topics we'll be covering this semester are: the central limit theorem, maximum likelihood estimation, method of moments estimation, confidence intervals, minimum-variance estimators, Cramer-Rao lower bound, sufficiency and consistency of estimators, hypothesis testing: binomial parameter, t test, Z test, generalized likelihood ratio, inferences about variances, two sample problems, goodness-of-fit tests, tests of independence and homogeneity, and nonparametric statistics.

Here is a link to the syllabus.

Here is a review of probability and some of the important distributions and their properties.

Office Hours: Mondays 12-1, Wednesdays 9-10, Fridays 3-4, or by appointment.

The text we'll use is An Introduction to Mathematical Statistics and Its Applications, 4th Edition, by Richard Larsen and Morris Marx. We'll finish chapter 4, then cover chapters 5-7, 9, 10, and some of 14.

Week |
Monday |
Wednesday |
Friday |

Jan. 17-20 |
MLK Day | 5.1 MLE introduction | 5.2 MLE examples HW1 assigned (due January 28) |

Jan. 24-28 |
5.2 more MLE |
5.2 more MLE MOM estimates |
5.3 confidence intervals HW1 solutions |

Jan. 31- Feb. 4 |
class canceled |
5.3 more confidence intervals |
5.4 unbiasedness |

Feb. 7-11 |
5.5 CRLB |
5.5 MVUE's HW2 solutions |
5.6 sufficiency |

Feb. 14-18 |
5.6, 5.7 consistency |
5.7 |
6.2 intro to hypothesis testing HW3 solutions |

Feb. 21-25 |
Exam 1 |
intro continued | hyp. testing: means (known variance) |

Feb. 28- Mar. 4 |
hyp. testing: proportions (started) | proportions (finished), P-values | Type I and II errors, power |

Mar. 7-11 |
spring break |
spring break |
spring break |

Mar. 14-18 |
more on alpha, beta, power: sample size | non-Normal data hyp. test vs CI |
estimators for mu, sigma Normal gamma function review |

Mar. 21-25 |
Chi Square distribution
properties CI and hyp test for normal variance |
F and t distributions | F and t distributions |

Mar. 28- Apr. 1 |
t test and CI's for means HW4 solutions |
two sample t test for means | two sample test for variances |

Apr. 4- Apr. 8 |
two sample test for proportions HW5 solutions |
Exam 2 |
multinomial distributions HW6 |

Apr. 11-15 |
goodness of fit- known parameters |
goodness of fit-unknown
parameters |
more examples |

Apr. 18-22 |
Patriot's Day |
intro to contingency tables HW7 solutions |
Easter break |

Apr. 25-29 |
Easter break | Chi square test for independence |
sign test |

May 2-6 |
Wilcoxon signed rank test |
runs test for randomness |