jump to main area
:::
A- A A+

Seminars

Asymptotic theory for time series analysis

  • 2025-02-24 (Mon.), 10:30 AM
  • Auditorium, B1F, Institute of Statistical Science;The tea reception will be held at 10:10.
  • Online live streaming through Cisco Webex will be available.
  • Prof. Masanobu Taniguchi
  • Waseda University

Abstract

This talk consists of the following two parts(i)&(ii).

(i)Hellinger Distance Estimation for Non-Regular Spectra
For Gaussian stationary process, we derive the time series Hellinger distance for spectra f and g: T(f, g). Evaluating T(f_θ, f_θ+h) of the form O(h^α), we elucidate the 1/α-consistent asymptotics of the maximum likelihood estimator of θ for non-regular spectra. For regular spectra, we introduce the minimum Hellinger distance estimator \hat{θ} = arg minθ T(f_θ, gˆn), where gˆn is a nonparametric spectral density estimator. We show that \hat{θ} is asymptotically efficient, and more robust than the Whittle estimator. Small numerical studies will be provided.

(ii) The least squares estimator (LSE) seems a natural estimator of linear regression models.
Whereas, if the dimension of the vector of regression coefficients is greater than 1 and the residuals are dependent, the best linear unbiased estimator (BLUE), which includes the information of the covariance matrix Γ of residual process has a better performance than LSE in the sense of mean square error. As we know the unbiased estimators are generally inadmissible. In this talk, we propose a shrinkage estimator based on BLUE. Sufficient conditions for this shrinkage estimator to improve BLUE are also given. Furthermore, since Γ is infeasible, assuming that Γ has a form of Γ = Γ(𝜽), we introduce a feasible version of that shrinkage estimator with replacing Γ(𝜽) by Γ(̂ 𝜽).  Additionally, we give the sufficient conditions where the feasible version improves BLUE.
 

Joint work with Yujie Xue(Waseda University)

Please click here for participating the talk online.

Download

1140224 Prof. Masanobu Taniguchi.pdf
Update:2025-02-19 14:53
scroll to top