# Advanced Statistical Methods

This course introduces the main notions, approaches, and methods of nonparametric statistics. The main topics include smoothing and regularization, model selection and parameter tuning, structural inference, efficiency and rate efficiency, local and sieve parametric approaches. The study is mainly limited to regression and density models. The topics of this course form an essential basis for working with complex data structures using modern statistical tools.

Instructor: Vladimir Spokoiny

Instructor assistants: Sergey Samsonov, Nikita Puchkin

**Venue**: Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1 Moscow, Russia 121205

**Schedule**:

**April 9**, Tuesday, **12:30 – 15:30**, room E-R2-B5-**3007**

**April 11**, Thursday, **16:00 – 19:00,** room E-R2-B5-**3006**

All lecture materials can be found in the script (v. 25.02).

If you have any questions about the course, please, write to *asmcourse2018@gmail.com*.

**Grades for the course**

You can find your grade for the exam and for the course here.

**Exam**

The written exam will take place on **Wednesday, April 24,** **at 3 Kochnovsky Proezd, room 205 from 10:00 to 11:20**. The list of questions for the exam is available here. The questions are divided into three groups. On the exam, you will have to answer three questions, one from each group. The usage of any gadgets or literature on the exam is strictly prohibited. Do not hesitate to ask TA’s if it is not clear for you, what the answer for a particular question from the list should include.

**Important remark. **You need a pass to enter the HSE building. Here is the list of students, who are expected to come to the exam. We will provide the pass to HSE for all these students in this list. Do not forget to take your passport. If you are willing to come to the exam but did not find your name in the list, please, write to *asmcourse2018@gmail.com *as soon as possible.

**Grades for projects and homeworks (upd 15.04)**

You can find you grades for the homeworks and projects here. If you have any questions concerning the grades for the homeworks, please, write to *asmcourse@gmail.com*. The grade for the course is computed as 0.125 * H + 0.7 * E + 0.125 * B, where H is the sum of points for all homeworks (maximum 24 points), E is the grade for the exam/project (maximum 10 points) and B is the bonus for found misprints in the script. After that, the grade is rounded to the nearest integer and this is your final grade. The grades 10, 9 and 8 correspond to A, 7 and 6 correspond to B, 5 and 4 correspond to C and, finally, 3, 2 and 1 correspond to F.

**Projects (upd 1.04)**

All of you have an option to complete a project. Those students who pass the project successfully, obtain the highest grade for the exam. The detailed project description is given here (v 1.04, a misprint in the Step 2 is fixed). The project defense will take place on **April 3, Wednesday, at 3 Kochnovsky Proezd, room 205 from 15:00 to 18:00**. To choose the project, follow the link. The assessment criteria can be found here(v. 31.03). The project defense schedule is available here.

**Important remark. **In the case of inhomogeneous noise, you can use the values of all variances on the step 3, while compute the risk. However, on the step 4, when you estimate parameters and perform a model selection procedure, you are given only the mean value of the variances. Thus, you deal with the case of misspecified noise and should take a unit matrix multiplied by the mean variance as the covariance matrix, while construct the estimates.

**Homework 1 (deadline: February 14, Thursday, 16:00)**

Complete exercises **1.2.3, 1.3.1, 1.4.4 **and** 1.4.6** from the script.

Format: send a Word/LaTeX-based PDF to *asmcourse2018@gmail.com* or bring a hand-written document to the lecture. PDF scans of hand-written documents will not be accepted.

**Homework 2 (deadline: February 18, Monday, 16:00)**

Complete exercises **1.4.5, 1.4.7, 1.6.1 **and** 1.6.3** from the script.

Format: send a Word/LaTeX-based PDF to *asmcourse2018@gmail.com* or bring a hand-written document to the lecture. PDF scans of hand-written documents will not be accepted.

**Homework 3 (deadline: February 21, Thursday, 16:00)**

Complete exercises **4.2.2, 4.2.3, 4.3.3 **and** 4.3.5** from the script.

Format: send a Word/LaTeX-based PDF to *asmcourse2018@gmail.com* or bring a hand-written document to the lecture. PDF scans of hand-written documents will not be accepted.

**Homework 4 (deadline: February 25, Monday, 16:00)**

Complete exercises **4.5.1, 5.2.2, 5.4.1 **and** 5.4.2** from the script.

*asmcourse2018@gmail.com* or bring a hand-written document to the lecture. PDF scans of hand-written documents will not be accepted.

**Homework 5 (deadline: February 28, Thursday, 16:00)**

Complete exercises **5.4.5, 6.4.1, 6.4.2 **and** 6.4.3** from the script.

*asmcourse2018@gmail.com* or bring a hand-written document to the lecture. PDF scans of hand-written documents will not be accepted.

**Homework 6 (deadline: March 15, Friday, 23:59)**

Complete exercises **9.1.1, 9.1.2****, 9.1.3 **and** 9.2.1** from the script.

Format: send a Word/LaTeX-based PDF to *asmcourse2018@gmail.com*. PDF scans of hand-written documents will not be accepted.