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Posts

On a variation of the Hausman test

2 minute read

Published: August 22, 2021

In econometric, Hausman test is frequently used to test if two estimators are both consistent for an unknown model coefficient, under the condition that one estimator is more efficient than the other. In mathematical terms, suppose we have two estimators $\hat\beta_1$ and $\hat\beta_2$ for a model coefficient $\beta$, and $\hat\beta_1$ is asymptotically efficient (achieving the Cramer-Rao lower bound), according to Wikipedia, the testing statistics of the Hausman test is

On Borel and Lebesgue measurability

3 minute read

Published: November 12, 2015

Walter Rudin’s book is hard to read probably because of two characteristics in his style: he likes to start with great generality, and “sneak in” (well, every now and then) many important details/ideas in lemmas and theorems (even proofs), without explaining the ideas with extra text or example that under which context they are important (again, every now and then). Here I would like to make a comment on measure construction in his book “Real and Complex Analysis” (3 ed, 1986). The following numberings are from this book, unless otherwise stated.

log(n) factor in the uniform convergence rate of smoothing estimator

5 minute read

Published: November 02, 2015

Given data i.i.d. ${(X_i,Y_i)}_{i=1}^n$, nonparametric “quantile regression” estimator at level $\tau \in (0,1)$ the minimizer of the following empirical loss function

portfolio

Regularized stochastic algorithms with application to deep neural networks

The goal is to develop a family of provable stochastic algorithms for e.g. large scale optimization and training deep neural networks. The provability is established by probabilistic weak approximation and the ordinary differential equation theory.

Statistical inference within distributed or cloud data ecosystem

My goal is to develop methods that can be smoothly implemented in the ecosystem of data science, and perform provabiy accurate statistical analysis including hypothesis testing on statistical models and causal effect.

Nonparametric quantile regression in social science

I develop quantile regression methods for economic and financial datasets that allow nonparametric modeling and/or high dimensionality $p>n$.

Brain and lung image data analysis

Clinicians rely on medical imaging to make diagonosis. I develop machine learning methods that discover subtle patterns in brain fRMI and lung MRI.

publications

Quantile Regression in Risk Calibration

Chao, S.-K., Härdle, W. Wang, W. (2015). Quantile Regression in Risk Calibration, in Lee, C.-F., and Lee, J. C. (eds), Handbook of Financial econometrics and statistics, Springer, New York.

On High Dimensional Post-Regularization Prediction Intervals

Chao, S.-K., Ning, Y. and Liu, H. (2015). On High Dimensional Post-Regularization Prediction Intervals. Unpublished manuscript.

Confidence Corridors for Multivariate Generalized Quantile Regression

Chao, S.-K., Proksch, K., Dette, H. and Härdle, W. (2017). Confidence corridors for nonparametric multivariate generalized quantile regression. Journal of Business and Economic Statistics, 35(1): 70-85.

Quantile processes for semi and nonparametric regression

Chao, S.-K., Volgushev, S. and Cheng, G. (2017). Quantile Process for Semi and Nonparametric Regression Models. Electronic Journal of Statistics, 11(2): 3272-3331.

Multivariate factorizable expectile regression with application to fMRI data

Chao, S.-K., Härdle, W. and Huang, C. (2018). Multivariate Factorizable Expectile Regression with Application to fMRI Data. Computational Statistics and Data Analysis, 121: 1-19.

Distributed inference for quantile regression processes

Volgushev, S., Chao, S.-K. and Cheng, G. (2019). Distributed inference for quantile regression processes. Annals of Statistics, 47(3): 1634-1662.

A generalization of regularized dual averaging and its dynamics

Chao, S.-K. and Cheng, G. (2019). A generalization of regularized dual averaging and its dynamics. Arxiv: 1909.10072.

A note on the impact of news on US household inflation expectations

Wang B. Z., Sheen, J., Trück, S., Chao, S.-K. and Härdle, W. (2020). A note on the impact of news on US household inflation expectations. Macroeconomic Dynamics.

Simultaneous Inference for Massive Data: Distributed Bootstrap

Yu, Y., Chao, S.-K. and Cheng, G. (2020). Simultaneous Inference for Massive Data: Distributed Bootstrap. ICML 2020 (acceptance rate: 21.8%).

Directional Pruning of Deep Neural Networks

Chao, S.-K., Wang, Z., Xing, Y. and Cheng, G. (2020). Directional Pruning of Deep Neural Networks. Advances in Neural Information Processing Systems 33.

Distributed Bootstrap for Simultaneous Inference Under High Dimensionality

Yang, Y., Chao, S.-K.* and Cheng, G. (2021). Distributed Bootstrap for Simultaneous Inference Under High Dimensionality. Journal of Machine Learning Research (Forthcoming).

Simultaneous Inference of Partially Linear Error-in-Covariate Models: an Application to the U.S. Gasoline Demand

Kim, K. H., Chao, S.-K. and Härdle, W. (2021). Simultaneous Inference of Partially Linear Error-in-Covariate Models: an Application to the U.S. Gasoline Demand. Journal of Statistical Planning and Inference, 213: 93-105.

Factorisable Multitask Quantile Regression

Chao, S.-K., Härdle, W. and Yuan, M. (2021). Factorisable Multitask Quantile Regression. Econometric Theory, 37(4): 794-816.

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015