arXiv subjects

Paul Bekker

Publications and source records attributed to Paul Bekker.

2 recordsLinked to original sources

arXiv2020

Exact Testing of Many Moment Inequalities Against Multiple Violations

This paper considers the problem of testing many moment inequalities, where the number of moment inequalities ($p$) is possibly larger than the sample size ($n$). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using the maximum $t$ statistic. We observe that such tests can have low power if multiple inequalities are violated. As an alternative, we propose novel randomization tests based on a maximum non-negatively weighted combination of $t$ statistics. We provide a condition guaranteeing size control in large samples. Simulations show that the tests control size in small samples ($n = 30$, $p = 1000$), and often has substantially higher power against alternatives with multiple violations than tests based on the maximum $t$ statistic.

math.ST↗

arXiv2019

Sparse Unit-Sum Regression

This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines $\ell_0$- and $\ell_1$-regularization. We compute its solution by adapting a recent methodological innovation made by Bertsimas et al. (2016) for $\ell_0$-regularization in standard linear regression. In a simulation experiment we compare our approach to $\ell_0$-regularization and $\ell_1$-regularization and find that it performs favorably in terms of predictive performance and sparsity. In an application to index tracking we show that our approach can obtain substantially sparser portfolios compared to $\ell_1$-regularization while maintaining a similar tracking performance.

stat.ME↗