Statistics ( M.S. )

1. Training/Research Orientation

• Statistics
• Financial Mathematics and Actuarial Sciences
• Applied Probability

2. Program Duration and Credit

3 years in general, the maximum duration should not exceed 5 years (including the extension time).
30 credits in total, at least 20 compulsory credits.

3. Courses Requirements and Introduction

Basis of Measurement and Probability
Content: Measurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gathering information from the real world. This course focuses on a single theory of measurement for the various domains of science and technology in which measurement is involved by addressing the following main issues: What is the meaning of measurement? How do we measure? What can be measured? Measurement, which played a key role in the birth of modern science, can act as an essential interdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems in measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation of inter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. The course presents a unified probabilistic approach to many fields which may allow more rational and effective solutions to be reached.
Prerequisites: Functional Analysis, Probability and Statistics.
Time: Once a week in 120 minute lectures.

Advanced Mathematical Statistics
Content: Statistics is the art of making numerical conjectures about puzzling questions, and it has enhanced our understanding of how life works, helped us learn about each other, allowed control over some societal issues, and helped individuals make informed decisions. There is almost no area of knowledge that has not been advanced by statistical studies. Advanced mathematical statistics is a course for postgraduates who major in statistics or financial mathematics. This course covers theories and methods of statistical inference, such as estimation, confidence intervals, hypothesis testing, and Baysian analysis. Properties of the methods are also studied. The course also introduces students to fisher information, Kullback-Leibler information, sufficient statistics, complete statistics, decision theory, and large sample theory, Other topics covered include asymptotic efficiency of estimates, exponential families
Prerequisites: Probability and Statistics.
Time: Once a week in 120 minute lectures.

Econometrics
Content: Econometrics introduces the theory and application of the economic relationships and the quantitative laws of economic activities, which is based on the instruction of the economic theory and the mathematical and statistical method with the help of computer. It belongs to the discipline of Economics, and concentrats on constructing economic models. The main contents of this course are Linear regression model, multiple linear regression model, multi collinearity, heteroscedasticity, autocorrelation, distributed lag model and autoregressive model, dummy variable regression and so on.
Prerequisites: Probability and Statistics.
Time: Once a week in 120 minute lectures.

Time Series Analysis
Content: Time Series Analysis is an important branch of applied fields of probability and statistics, and has a wide application in a variety of fields, ranging from finance and economics, meteorology and hydrology to signal handle and mechanics. The main purpose of this course is to provide students with a rigorous theoretical foundation and empirical analysis skills to pursue applied projects involving economic and financial time series data, such as business applications (e.g., skillful usage of computer software packages) and research projects. The course focuses empirically and theoretically on time series methods that have become popular and are widely used in applied economics and finance. The content of this course mainly includes characteristics of time series, univariate stationary time series models, principles of forecasting, estimation and inference in stationary ARMA models, vector autoregressive models, co-integration, unit root processes, nonlinear time series models and so on. Meanwhile, this course also provides a detail introduction to the frontier of time series analysis to help students find suitable research topics.
Prerequisites: Probability and Statistics.
Time: Once a week in 120 minute lectures.

Risk Theory and Stochastic Control
Content: The first part of this course focuses on the introduction of the classical risk models as well as the diffusion approximation risk model and risk model with some control variables, such as, reinsurance and investment. The second part of this course mainly introduces the basic principles of stochastic control, some classical problems in diffusion control, and some optimal stopping problems as well as impulse control problems.
Prerequisites: Stochastic processes and stochastic calculus
Time: Once a week in 160 minute lectures.

4. Supervisors

Xiuli Du, Qibing Gao, Zhibin Liang, Guoxiang Liu, Hui Mi, Xiaoqian Wang, Fengchang Xie, Xiaoming Xu, Yi Yao, Yuanyuan Zhao, Xiuqing Zhou, Quanxin Zhu.