Department of Statistics
Stat 2630: Introduction to Mathematical Statistics Using R
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Instructor: Joshua D. Naranjo E-mail: joshua.naranjo@wmich.edu Phone: (269)387-4548 Office: 5507 Everett Tower |
Tuesday, March 10
- Notes (Hypothesis Testing 6: Tests of Homogeneity and Independence)
- Homework 14
Spring Break (March 2-6)
- Notes (Hypothesis Testing 5: Chi-square Goodness-of-Fit)
- Homework 13
- Exer. 4.7.3 (Normal Goodness-of-fit)
- Exer. 4.7.9 (Poisson Goodness-of-fit)
- Midterm Exam
Thursday, Feb. 20
- Notes (Hypothesis Testing 4: Wilcoxon Rank Sum )
- BMR handout
- Notes (Hypothesis Testing 3: Behrens-Fisher, Dependent means and proportions)
- Homework 12
- R code for Welch-t vs pooled-t power simulation
- Notes (Hypothesis Testing 2: Two-sided tests, p-value)
- Homework 11
- Exer. 4.6.4
- Exer. 4.6.7
- Notes (Hypothesis Testing: size and power)
--plot()
--lines() (for overlay of two plots)
--legend()
- Homework 10
- Notes (Interval Estimation 2: Proportions, Two-sample)
--t.test()
--load()
- Homework 9
- Notes (Interval Estimation: One-sample mean)
- R simulation: z versus t distribution
--apply()
--hist() (overlayed histogram) - R simulation: The Central Limit Theorem
- Homework 8
- Exer. 4.2.1
- Exer. 4.2.2
- Exer. 4.2.8
- Recommended problems: 4.2.3 (b,c)
- The following paper uses both SD and SE of the mean. The SD is used to simply describe data (Table 1). The SE of the mean is used for inference, as a measure of "closeness" of the estimate (Table 2).
- Notes (MLE, density estimates)
- Homework 7
- Exer. 4.1.2 (c,d)
- Exer. 4.1.8
- The following papers use kernel density estimation
- Notes (Point Estimation, MLE)
--for()
--function()
--optimize() - HW 5 simulation in R
--apply()
--hist() (overlayed histogram) - Homework 6: Let X be Poisson with parameter lambda. Suppose we have the following n=10 observations
9, 7, 9, 15, 10, 13, 11, 7, 2, 12 - Write the likelihood as a function in R, and plot the likelihood. Use lambda values from 1 to 20.
- Use optimize in R to calculate the value of theta that maximizes the likelihood. Does this agree with the plot?
- Find the MLE analytically by taking derivative and equating to 0. Does this agree with the value you found numerically?
- This paper uses both means and proportions to compare treatment and control groups (see Table 1)
- Notes (Special Continuous Distributions)
- Homework 5
- Exer. 3.3.6
- Exer. 3.4.8
- R code for Gamma, Chi-square, normal
- Notes (Special Discrete Distributions)
- Homework 4
- Exer. 3.1.5
- Exer. 3.1.30 (a,b)
- Exer. 3.2.3
- Recommended problems: 3.1.1, 3.1.4, 3.1.8, 3.1.30 (c), 3.2.6, 3.2.8
- R code for binomial, hypergeometric, Poisson
- Notes (Mean, Variance, mgf)
- Recommended problems: 1.9.1 (a,b), 1.9.2, 1.9.3
- Notes (Random Variables and Expectation)
- Homework 3
- Exer. 1.7.14 (p.59)
- Exer. 1.7.22 (p.60)
- Notes (Conditional probability and Independence)
- Homework 2
- Exer. 1.4.8 (p.33)
- Exer. 1.4.14 (p.34)
- Notes (Counting rules)
- Syllabus (pdf)
- Homework 1
- Exer. 1.3.10 (p.21)
- Exer. 1.3.13 (p.22)
- Recommended problems: 1.3.3, 1.3.4, 1.3.14, 1.3.15, 1.3.19
- R code for birthday problem (Copy into script window)
- HMC web page (datasets and R functions)