All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly. This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the Honor Code, students are obligated to report any such activities to the Instructor.
Mathematics 762-102:
Statistical inference
Spring 2007
Instructor: Prof.
Dhar
Prerequisite: This course is part of the Math 662 - Math 762
sequence. Prerequisite of Math 662 must be satisfied.
Textbook: Introduction to Mathematical Statistics (Sixth
Edition) by Robert V. Hogg, Joseph W. McKean and Allen T. Craig; ISBN: 0-13-008507-3.
Grading Policy: The final grade in this course will be determined as
follows:
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☑ Quizzes + Homework: |
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20% |
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☑ Midterm Exam: |
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40% |
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☑ Final Exam: |
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40% |
Course
grade evaluates all knowledge gained in Math 762 therefore its understanding
must be continually worked upon. Solving problems from the text and learning
solved examples therein even when they are not assigned as homework/quizzes,
etc. The course is based upon problem solving.
Reference:
1. Probability and Statistical Inference by Nitis Mukhopadhyay, 2000, Marcel
and Dekker, Inc. ISBN: 0-8247-0379-0
2. Introduction to the Theory of Statistics, by Mood, Graybill and Boes, Third edition.
3. Probability and Statistics, by Morris H. DeGroot and Mark J. Schervish,
Third Edition
4. A Course in Mathematical Statistics, George G. Roussas, Second Edition.
(Has certain solutions to both odd and even problems)
5. Fundamentals of Probability, Saeed
Ghahramani, Second Edition, Prentice Hall
Attendance and Participation: Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.
Makeup Exam Policy: There will be no makeup exams, except in rare situations where the student has a legitimate reason for missing an exam, including illness, death in the family, accident, requirement to appear in court, etc. The student must notify the Math office and the Instructor that he/she will miss an exam. In all cases, the student must present proof for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
Additional
Policies:
☑
Any complaints regarding
grading have to be presented immediately after receiving the graded tests.
☑
Please, always bring a
statistics calculator to your quizzes, exams and to all the lectures. However, you are not allowed to bring a
calculator that has a visual display in exams and quizzes.
☑
Looking into your
neighbors work during exams is not allowed. Keeping eyes hidden using hats,
caps, etc., from the proctor but not from the neighbors work during exams is
not allowed.
☑
Attendance at all classes
and tests is required. Instructors will maintain a detailed record of you
attendance as the administrators need to know the dates you missed classes.
☑
The use of cell phones,
beepers, or any sort of communication devices (laptops, internet, palm pilot,
etc) during exams and quizzes are not allowed.
☑
No eating allowed during
the class and exams periods. You are expected to remain in the classroom for
the entire class period. Wandering in and out of the classroom is not allowed.
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Week 1 |
Distribution
Theory Background |
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☑ Weak law of large numbers,
Central Limit Theorem, Bounded in Probability, Delta Method and Moment
Generating Function Technique for Proving Distribution Convergence. |
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Week 2 |
Some Elementary
Statistical Inference |
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☑ Sampling and Statistics, Order
Statistics. |
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☑ Confidence Intervals,
Introduction to Hypothesis Testing. |
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Week 3 |
Some
Elementary Statistical Inference |
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☑ Confidence Interval of
Difference in Mean or Proportions. |
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☑ Fundamental Concepts and
Principles of Testing (Classification of Hypotheses, Test Functions, Critical
Regions, Size and Power, p-value). |
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Week 4 |
Maximum
likelihood Methods |
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☑ Rao-Cramer Lower Bound and Efficiency.
Statistical Functionals and Plug-in Estimators. |
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☑ Method of Moments and its
Properties, Examples. |
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Week 5 |
Maximum
likelihood Methods |
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☑ Maximum Likelihood Tests. |
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☑ Multiparmeter Case: Estimation and Testing. |
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Week 6 |
Sufficiency |
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☑ Data Reduction Principles,
Likelihood and Sufficiency. |
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☑ Completeness and Uniqueness,
Minimum Variance Unbiased (MVU) estimators. |
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Week 7 |
◄ Midterm EXAM ► |
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Optimal Tests
of Hypotheses |
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☑ Most Powerful Tests, Neyman-Pearson Lemma. |
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◄◄SPRING
RECESS: March 12-16, 2007 |
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Week 8 |
Optimal Tests
of Hypotheses |
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☑ Likelihood Ratio Tests. |
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☑ Monotone Likelihood Ratio and
Uniformly Most Powerful Tests. |
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Week 9 |
|
|
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Inference
about normal models |
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☑ Quadratic Forms, One-way
Analysis of Variance. |
|
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☑ Non-central Chi-squared and F
Distributions. |
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Week 10 |
Inference
about normal models |
|
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☑ Multiple Comparisons |
|
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☑ A Test for |
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Week 11 |
Introduction
to Regression Modeling |
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☑ Linear Regression, Logistic
Regression |
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Week 12 |
Nonparametric
Statistics |
|
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☑ Location models, Sample Median,
Signed-Rank Wilcoxon, Mann-Whitney-Wilcoxon Procedure Pearson Chi-square Test for Frequency
Data. |
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Week 13 |
Nonparametric
Statistics |
|
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☑ Goodness-of-fit tests, Testing
for Independence of Two Variables |
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Week 14 |
☑ COURSE
REVIEW FOR FINAL EXAM |
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FINAL EXAM: MONDAY May 7, 2007 ~ 6:00 pm – 8:30 pm |
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Last
revised:
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January 15 |
M |
MLK
Day – No Classes Scheduled |
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March 26 |
M |
Last Day to Withdraw from Classes |
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April 6 |
F |
Good
Friday – No Classes Scheduled |
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May 1 |
T |
Classes Follow a Friday
Schedule |