AMS 412, Mathematical Statistics
Catalog Description: Estimation, confidence intervals, Neyman Pearson lemma, likelihood ratio test, hypothesis
testing, chi square test, regression, analysis of variance, nonparametric methods.
Prerequisite: AMS 311
3 credits
SBC: CER, ESI, EXP+
Required Textbook:
"Mathematical Statistics with Applications" by Kandethody Ramachandran & Chris P.
Tsokos; 2nd Edition; Publisher: Elsevier/Academic Press, 2015;
ISBN: 978-0-12417113-8
AMS 412 Instructor page
THIS COURSE IS TAUGHT IN THE SPRING SEMESTER AND SUMMER SESSION STARTING 2020
Topics
1. Point Estimation (first half of Chap. 8) – 4 class hours.
2. Sampling Distributions (Chap. 7) – 2 class hours.
3. Properties of Point Estimators and Methods of Estimation (Chap. 9) – 8 class
hours.
4. Interval Estimation (second half of Chap. 8) – 6 class hours.
5. Hypothesis Testing (Chap. 10) – 7 class hours
6. Linear Models and Least Squares (Chap. 11) – 6 class hours.
7. Analysis of Variance (Cap. 13) –5 class hours.
8. Examinations and Review – 4 class hours.
Learning Outcomes for AMS 412, Mathematical Statistics
1.) Demonstrate an understanding of point estimation and its applications – beginning
of the learning of statistical inference:
* the method of moment estimator (MOME);
* the maximum likelihood estimator (MLE);
* order statistics and their application in deriving the MLE;
* the difference between the MOME and the MLE;
* unbiasedness, the minimum variance unbiased estimator (MVUE) and the Cramer-Rao
Lower Bound (to identify efficient estimator, best estimator).
2.) Demonstrate an understanding of confidence intervals and their applications –continuing
the learning of statistical inference:
* pivotal quantity;
* variable transformation techniques especially the moment generating function
technique;
* confidence interval for one population mean (including paired samples) and
for one populatin variance when the population distribution is normal;
* large sample confidence interval using the Central Limit Theorem with focus
on CI for one population mean (including paired samples), and one population proportion;
* confidence interval for a modified problem for one population mean or proportion
or variance;
* the right confidence intervals for real world problems.
3.) Demonstrate an understanding of hypothesis testing and its applications –continuing
the learning of statistical inference:
* hypothesis testing including the type I and II errors, significance level,
rejection region, effect size, power of the test, and p-value;
* hypothesis test using the pivotal quantity method for one population mean
(including paired samples) and one population variance when the population distribution
is normal;
* large sample hypothesis test using the pivotal quantity method and the Central
Limit Theorem for one population mean (including paired samples) or proportion;
* hypothesis test using the likelihood ratio test method for one population
mean and for one population variance when the population distribution is normal;
* hypothesis test using the likelihood ratio test method for one population
proportion;
* asymptotic distribution of the likelihood ratio test;
* relationship between tests derived using the likelihood ratio test method
and the pivotal quantity method;
* hypothesis test for a modified problem for one population mean or proportion
or variance;
* right hypothesis tests for real world problems.
4.) Undertake group statistical projects involving one of the following topics, including
written and spoken presentation of results:
* confidence interval and hypothesis tests for two population means, variances
or proportions based on independent samples;
* non-parametric tests for one mean, two means and several means, and the
Spearman rank correlation;
* one-way ANOVA;
* simple linear regression and the Pearson product moment correlation;
* multiple linear regression.