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Math 665: Statistical Inference
Spring 2018 Graduate Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that 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 University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

Course Information

Course Description: Review of sampling distributions. Data reduction principles: sufficiency and likelihood. Theory and methods of point estimation and hypothesis testing, interval estimation, nonparametric tests, introduction to linear models.

Number of Credits: 3

Prerequisites: MATH 662 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 665-102 Professor S. Subramanian

Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails

Required Textbooks:

Title Introduction to Mathematical Statistics
Author Hogg, McKean, and Craig
Edition 7th
Publisher Pearson
ISBN # 978-0321795434

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 2, 2018. It will be strictly enforced.

Course Goals

Course Objectives and Description: This course will focus on mathematical methods for statistical inference. Topics include review of sampling distributions, data reduction principles: sufficiency and likelihood, theory and methods of point estimation and hypothesis testing, interval estimation, bootstrap procedures and the EM algorithm.

Course Outcomes: On successful completion, students will be able to demonstrate understanding of the following topics:

Course Assessment: Will be based on regular homework, two midterm exams, and one final exam.


DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.

Grading Policy: The final grade in this course will be determined as follows:

Homework 25%
Midterm Exams 40%
Final Exam 35%

Your final letter grade will be based on the following tentative curve.

A 90 - 100 C+ 75 - 79
B+ 85 - 89 C 66 - 74
B 80 - 84 F 0 - 65

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Homework Policy: Homework assignments are due within a week unless announced otherwise by instructor.   Late homework will not be accepted.

Exams: There will be two midterm exams held in class during the semester and one comprehensive final exam. Exams are held on the following days:

Midterm Exam I February 27, 2018
Midterm Exam II April 10, 2018
Final Exam Period May 4 - 10, 2018

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Additional Resources

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall, Room 260.  A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

Course Outline

Week Date Topic
Week  1
Chapter 5 Consistency and limiting distributions
Consistency; central limit theorem; delta method; moment generating functions  
Week 2
Chapter 4 Some Elementary Statistical Inference
Sampling and statistics; confidence intervals; hypothesis testing.
Week 3
Chapter 6 Maximum likelihood Methods
Rao-Cramer lower bound and efficiency; plug-in estimators; method of moments
Week 4
Chapter 6 Maximum likelihood Methods
Maximum likelihood tests; multiparameter case: estimation and testing
Week 5
Chapter 7 Sufficiency
Sufficient statistic and properties: Rao Blackwell; completeness and uniqueness
Week 6
Chapter 7 Sufficiency (continued)
Minimum variance unbiased estimators; exponential family; functions of a parameter
Week 7
TUESday ~ FebrUARY 27, 2018
Week 8
Chapter 7 Sufficiency (continued)
Minimal sufficiency; ancillary statistics. Sufficiency, completeness and independence
Week of 3/12 Spring recess ( No classes)
Week 9
Chapter 8 Optimal Tests of Hypotheses
Most powerful tests; Neyman-Pearson lemma
Week 10
Chapter 8 Optimal Tests of Hypotheses (continued)
Uniformly most powerful tests; likelihood ratio tests; monotone likelihood ratio 
Week 11
Chapter 8 Optimal Tests of Hypotheses (continued)
The sequential probability ratio test
Week 12
TUESday ~ April 10, 2018
Week 13
Chapter 4 Bootstrap procedures
Week 14
Chapter 5 The EM algorithm
Week 15
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Updated by Professor S. Subramanian - 1/18/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018