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AbstractKernel regularized least squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing approaches are inflexible and do not allow KRLS to be combined with theoretically motivated extensions such as random effects, unregularized fixed effects, or non-Gaussian outcomes. Second, estimation is extremely computationally intensive for even modestly sized datasets. Our paper addresses both concerns by introducing generalized KRLS (gKRLS). We note that KRLS can be re-formulated as a hierarchical model thereby allowing easy inference and modular model construction where KRLS can be used alongside random effects, splines, and unregularized fixed effects. Computationally, we also implement random sketching to dramatically accelerate estimation while incurring a limited penalty in estimation quality. We demonstrate that gKRLS can be fit on datasets with tens of thousands of observations in under 1 min. Further, state-of-the-art techniques that require fitting the model over a dozen times (e.g., meta-learners) can be estimated quickly.

AbstractIn this article we propose a new parsimonious state‐space model in which state variables characterize the stochastic movements of stock returns. Using the equally weighted and decile monthly stock returns, we show that (a) a parsimonious state‐space model characterizes the variation in expected returns at any horizon; (b) the extracted expected returns explain a substantial proportion of the variance in realized returns, and the magnitude of this proportion increases significantly with the horizon of returns; (c) the model successfully captures the empirical fact that returns of smaller firms have both stronger positive autocorrelations of short‐horizon returns and stronger negative autocorrelations of long‐horizon returns; and (d) the forecasts of asset returns obtained with the state‐space model subsume the information in other potential predictor variables such as dividend yields.JEL classification: G10, G12.

Xian Chang,1,* Yang-Fan Lv,2,* Jing He,3,* Ya Cao,2 Chang-Qing Li,1 Qiao-Nan Guo2 1Department of Orthopedics, Xinqiao Hospital, Third Military Medical University (Army Medical University), Chongqing, 400037, People's Republic of China; 2Department of Pathology, Xinqiao Hospital, Third Military Medical University (Army Medical University), Chongqing, 400037, People's Republic of China; 3Department of Pediatric Surgery, Guangzhou Institute of Pediatrics, Guangdong Provincial Key Laboratory of Research in Structural Birth Defect Disease, Guangzhou Women and Children's Medical Center, Guangzhou Medical University, Guangzhou, 510623, Guangdong, People's Republic of China*These authors contributed equally to this workCorrespondence: Qiao-Nan Guo; Chang-Qing Li Email qiaonan85@263.net; changqli1970@126.comBackground: N6-methyladenosine (m6A) RNA methylation is the most prevalent modification of mammalian RNA, and it is associated with tumorigenesis and cancer progression. Its regulation is mediated via m6A-related regulators, including "erasers," "readers," and "writers". The present study evaluated the expression profile, risk signature and prognostic value of 13 m6A regulators in hepatocellular carcinoma (HCC) using different datasets, including The Cancer Genome Atlas (TCGA), Gene Expression Omnibus (GEO) and clinical samples.Methods: We used 374 HCC samples derived from the TCGA database, 569 HCC samples from 2 GEO datasets, and clinical tumour and nontumour tissues derived from 60 patients with HCC who underwent surgery in Xinqiao Hospital Chongqing to assess the gene expression profiles and prognostic values of m6A-related regulators in HCC.Results: Eight of 13 core m6A-related regulators were overexpressed in all databases, including TCGA, GSE, clinical tumour and nontumour tissues of HCC. Two clusters (Cluster 1 and Cluster 2) were identified via consensus clustering. Cluster 2 was associated with poorer prognosis, higher tumour grade, higher AFP levels, and worse outcome compared to Cluster 1, which indicates that these m6A-related regulators are highly correlated with HCC malignancy. We performed survival analyses using the Log rank tests and a Cox regression model. Gene enrichment analysis was used to detect the related KEGG and GO pathways. We derived a prognostic risk signature using five selected m6A-related regulators.Conclusion: Our work suggested that m6A-related regulators might be key participants in the tumour progression of HCC and potential biomarkers with prognostic value.Keywords: RNA modification, N6-methyladenosine, m6A, hepatocellular carcinoma, prognosis, RNA methylation regulators