Statistics

Statistics Seminar Series

Statistics is all about getting data and analysing it and using it to answer questions about the world be that in terms of Economics, Finance or public opinions. The applications are numerous

The Department of Statistics hosts this Statistics Seminar Series throughout the year and usually taking place on Friday afternoons at 3pm. Topics include statistical methodology, theory, and applications. All are welcome to attend as we are currently holding these seminars remotely. 

Michaelmas Term 2021 

Friday 8 October 2021, 2-3pm - Professor Fang Yao
Please note the earlier time of a 2pm start for this week only. 

Yao-image

Biography: https://www.math.pku.edu.cn/teachers/yaof/

Title: Functional Linear Regression for Discretely Observed Data: From Ideal to Reality. 

Absract: In this work, we give a new insight into estimation and prediction issues in functional linear regression (FLR) when the covariate process is discretely observed with noise. Without the fully observed functional data, it is difficult to derive a sharp bound for the estimated eigenfunctions, which makes the existing techniques for FLR unfeasible.  We use pooling method to attain the estimated eigenfunctions without pre-smoothing each curve and propose a sample-splitting approach to estimate the component scores, which is novel for treating discretely observed data and facilitate the theoretical analysis. We then obtain the estimated slope function by the approximated least squared method. We show that the proposed method attains the optimal convergence rate as if the curves are fully observed for slope estimation and prediction error when the number of measurements per subject reach the magnitude which is determined the smoothness of the covariance and slope function, where is the number of subjects. This phase transition of the convergence rate is always between and , which differs from the phase transition of the pooled mean and covariance estimation at and reveals the elevated difficulties in estimating the slope function. We also evaluate the numerical performance of our proposed method using simulated and real data examples, yielding similar or favorable results when contrasted to comparable methods. 

➡️Register here! 

 

Lent Term 2022

To be confirmed.