**Math ****786**: Large Sample Theory and Inference

*Fall 2017 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**: Limit theorems, central limit theorem, asymptotic expansions and large deviations, limit theorems in martingales and semi-martingales and stochastic differential equations, asymptotic expansions of functions of statistics, linear parametric estimation, asymptotic efficiency, martingale approach to inference: test for homogeneity and goodness of fit, decomposable statistics, inference for counting processes and censored data, inference in nonlinear regression, existence and consistency of least squares estimator (LSE), asymptotic properties of LSE, Von Mises functionals, estimation of parameters of stable laws, empirical characteristics function for inference, generalized least squares for linear models.

**Number of Credits**: 3

**Prerequisites**: MATH 662.

**Course-Section and Instructors**

Course-Section |
Instructor |

Math 786-001 |
Professor S. Subramanian |

**Office Hours for All Math Instructors**: Fall 2017 Office Hours and Emails

**Required Textbooks**:

**Title** |
*Approximation Theorems of Mathematical Statistics* |

**Author** |
Serfling |

**Edition** |
1st |

**Publisher** |
Wiley |

**ISBN #** |
978-0471219279 |

**University-wide Withdrawal Date**:The last day to withdraw with a **w** is **Monday, November 6, 2017**. It will be strictly enforced.

## Course Goals/ EXTRA INFORMATION

**Course Objectives and Description**: This course will be concerned with teaching doctoral level mathematical sciences students the rudiments of statistical large sample theory, focusing on a variety of limit theorems and techniques useful in mathematical statistics. Topics covered will be asymptotic distributions of estimators such as sample moments and quantiles, order statistics, and maximum likelihood; projection and U statistics; empirical processes; functional delta method; and nonparametric density estimation.

### Course Outcomes

- Methods of proof and techniques of application of limit theorems in statistics;

- Large-sample theory for sample moments, quantiles, and empirical distribution functions;

- The delta method and its functional version;

- Hajek projections, Hoeffding decomposition and U statistics;

- Empirical Processes.

**Course Assessment**: Will be based on regular homework, one midterm exam, and a final in-class presentation of a course-specific rigorous research topic assigned by instructor.

## Policies

**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** |
30% |

**Midterm Exam** |
40% |

**Final Exam** |
30% |

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

**A** |
85 - 100 |
**C**+ |
70 - 74 |

**B+** |
80 - 84 |
**C** |
60 - 73 |

**B** |
75 - 79 |
**F** |
0 - 59 |

**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 one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:

Midterm Exam |
November 8, 2017 |

Final Exam Period |
December 15 - 21, 2017 |

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 lyles@njit.edu. 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: Fall 2017 Academic Calendar, Registrar)

Date |
Day |
Event |

September 5, 2017 |
T |
First Day of Classes |

September 11, 2017 |
M |
Last Day to Add/Drop Classes |

November 6, 2017 |
M |
Last Day to Withdraw |

November 21, 2017 |
T |
Thursday Classes Meet |

November 22, 2017 |
W |
Friday Classes Meet |

November 23 - 26, 2017 |
R - Su |
Thanksgiving Break - University Closed |

December 13, 2017 |
W |
Last Day of Classes |

December 14, 2017 |
R |
Reading Day |

December 15 - 21, 2017 |
F - R |
Final Exam Period |