Downloads
![Image representing the file: cwp461414.pdf](/sites/default/files/output_url_files/cwp461414.pdf_0.jpg)
cwp461414.pdf
PDF | 675.68 KB
We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n= log n)–p=(2p+d) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 + (d=p))th absolute moment for d=p 2.We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.
Authors
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Yale University
![Timothy Christensen](/sites/default/files/styles/square_desktop/public/2022-07/Timothy%20Christensen.jpg?itok=OVzNRflX)
Research Associate University College London, Cemmap
Timothy is a Research Associate at IFS and a Professor of Economics at University College London.
Working Paper details
- DOI
- 10.1920/wp.cem.2014.4614
- Publisher
- IFS
Suggested citation
Chen, X and Christensen, T. (2014). Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions. London: IFS. Available at: https://ifs.org.uk/publications/optimal-uniform-convergence-rates-and-asymptotic-normality-series-estimators-under (accessed: 1 July 2024).
More from IFS
Understand this issue
![State Pension claim form](/sites/default/files/styles/square_desktop/public/2023-12/state-pension-claim-form.jpg?itok=OCixJu9J)
Where next for the state pension?
13 December 2023
![Nice houses with city in the background](/sites/default/files/styles/square_desktop/public/2023-12/nice-houses-with-city-in-background_0.jpg?itok=TDx-TwSe)
Social mobility and wealth
12 December 2023
![Chancellor Jeremy Hunt with red box](/sites/default/files/styles/square_desktop/public/2023-12/chancellor-jeremy-hunt-with-red-box.jpg?itok=Dah5hdYC)
Autumn Statement 2023: IFS analysis
23 November 2023
Policy analysis
![Welsh town with mountains behind](/sites/default/files/styles/square_desktop/public/2024-06/Welsh-town-feature.jpg?itok=5axb5wZn)
How would the parties’ tax and spending plans affect Scotland and Wales?
28 June 2024
![Man putting vote into ballot box](/sites/default/files/styles/square_desktop/public/2022-07/Man-putting-vote-into-ballot-box.jpg?itok=Pa6g41dr)
General Election 2024: Manifesto Analysis Presentations
24 June 2024
![Shopping street](/sites/default/files/styles/square_desktop/public/2024-06/Street-scene-.jpg?itok=R39cR6Xp)
How do the last five years measure up on levelling up?
19 June 2024
Academic research
![Working paper cover](/sites/default/files/styles/portrait/public/2024-06/WP202428-The-impact-of%20labour-demand-shocks-when-occupational-labour-supplies-are-heterogeneous.jpg?itok=Erq9-V9O)
The impact of labour demand shocks when occupational labour supplies are heterogeneous
28 June 2024
![Working Paper Cover](/sites/default/files/styles/portrait/public/2024-06/WP202427-The-impact-of-flexibility-at-work-on-fertility_Page_01.jpg?itok=pHaEvbkK)
The impact of flexibility at work on fertility
11 June 2024
![Working Paper Cover](/sites/default/files/styles/portrait/public/2024-06/WP202426-Intergenerational-mobility-in-socio-emotional-skills_Page_01.jpg?itok=wH1znQhh)
Intergenerational mobility in socio-emotional skills
5 June 2024