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This paper develops a general framework for estimation of high-dimensional conditional factor models via nuclear norm regularization. We establish large sample properties of the estimators, and provide an efficient computing algorithm for finding the estimators as well as a cross validation procedure for choosing the regularization parameter. The general framework allows us to estimate a variety of conditional factor models in a unified way and quickly deliver new asymptotic results. We apply the method to analyze the cross section of individual US stock returns, and find that imposing homogeneity may improve the model's out-of-sample predictability., Comment: 50 pages

Gluons may converge to a stable state at a critical momentum in hadrons. This gluon condensation is predicted by a nonlinear QCD evolution equation. We review the understanding of the gluon condensation and present a clear physical picture that produces the gluon condensation from the colour glass condensate. We summarize the applications of the GC effect in the $p-p(A)$ collisions and predict that the $p-Pb$ and $Pb-Pb$ collisions at the LHC are close to the energy region of the gluon condensation. We warn that for the next generation of hadron colliders with the increasing of the collision energy, the extremely strong gamma-rays will be emitted in a narrow space of the accelerator due to the gluon condensation effect. Such artificial mini gamma-ray bursts in the laboratory may damage the detectors., Comment: 30 pages, 11 figures, 2 tables, Accepted for publication in NPB. arXiv admin note: text overlap with arXiv:2109.09826

This paper develops estimation and inference methods for conditional quantile factor models. We first introduce a simple sieve estimation, and establish asymptotic properties of the estimators under large $N$. We then provide a bootstrap procedure for estimating the distributions of the estimators. We also provide two consistent estimators for the number of factors. The methods allow us not only to estimate conditional factor structures of distributions of asset returns utilizing characteristics, but also to conduct robust inference in conditional factor models, which enables us to analyze the cross section of asset returns with heavy tails. We apply the methods to analyze the cross section of individual US stock returns., Comment: 55 pages. arXiv admin note: text overlap with arXiv:2112.07121

This paper introduces a simple and tractable sieve estimation of semiparametric conditional factor models with latent factors. We establish large-$N$-asymptotic properties of the estimators without requiring large $T$. We also develop a simple bootstrap procedure for conducting inference about the conditional pricing errors as well as the shapes of the factor loading functions. These results enable us to estimate conditional factor structure of a large set of individual assets by utilizing arbitrary nonlinear functions of a number of characteristics without the need to pre-specify the factors, while allowing us to disentangle the characteristics' role in capturing factor betas from alphas (i.e., undiversifiable risk from mispricing). We apply these methods to the cross-section of individual U.S. stock returns and find strong evidence of large nonzero pricing errors that combine to produce arbitrage portfolios with Sharpe ratios above 3. We also document a significant decline in apparent mispricing over time., Comment: 112 pages

We develop a Stata command, bootranktest, for implementing the matrix rank test of Chen and Fang (2019) in linear instrumental variable regression models. Existing rank tests employ critical values that may be too small, and hence may not even be first order valid in the sense that they may fail to control the Type I error. By appealing to the bootstrap, they devise a test that overcomes the deficiency of existing tests. The command bootranktest implements the two-step version of their test, and also the analytic version if chosen. The command also accommodates data with temporal and cluster dependence.

This paper presents a unified second order asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\theta_0$ is unknown but can be estimated by $\hat\theta_n$, and $\phi$ is a known map that admits null first order derivative at $\theta_0$. For a large number of examples in the literature, the second order Delta method reveals a nondegenerate weak limit for the plug-in estimator $\phi(\hat\theta_n)$. We show, however, that the `standard' bootstrap is consistent if and only if the second order derivative $\phi_{\theta_0}''=0$ under regularity conditions, i.e., the standard bootstrap is inconsistent if $\phi_{\theta_0}''\neq 0$, and provides degenerate limits unhelpful for inference otherwise. We thus identify a source of bootstrap failures distinct from that in Fang and Santos (2018) because the problem (of consistently bootstrapping a \textit{nondegenerate} limit) persists even if $\phi$ is differentiable. We show that the correction procedure in Babu (1984) can be extended to our general setup. Alternatively, a modified bootstrap is proposed when the map is \textit{in addition} second order nondifferentiable. Both are shown to provide local size control under some conditions. As an illustration, we develop a test of common conditional heteroskedastic (CH) features, a setting with both degeneracy and nondifferentiability -- the latter is because the Jacobian matrix is degenerate at zero and we allow the existence of multiple common CH features.

This paper develops a general framework for conducting inference on the rank of an unknown matrix $\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\mathrm H_0: \mathrm{rank}(\Pi_0)\le r$. The problem is of first order importance because the previous literature focuses on $\mathrm H_0': \mathrm{rank}(\Pi_0)= r$ by implicitly assuming away $\mathrm{rank}(\Pi_0)