Regression with a Slowly Varying Regressor in the Presence of a Unit Root

This paper considers the regression model with a slowly varying (SV) regressor in the presence of a unit root in serially correlated disturbances. This regressor is known to be asymptotically collinear with the constant term; see Phillips (2007). Under nonstationarity, we find that the estimated coefficients of the constant term and the SV regressor are asymptotically normal, but neither is consistent. Further, we derive the limiting distribution of the unit root test statistic. We may here observe that the finite sample approximation to the limiting one is not monotone and it is poor due to the influence of the collinear regressor. In order to construct a well-behaved test statistic, we recommend dropping the constant term intentionally from the regression and computing the statistics, which are still consistent under the true model having the constant term. The powers and sizes of these statistics are found to be well-behaved through simulation studies. Finally, these results are extended to general Phillips and Perron-type statistics.

Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices

This paper presents a time series model that has an asymptotically efficient ordinary least squares (OLS) estimator, irrespective of the singularity of its limiting sample moment matrices. In the literature on stationary time series analysis, Grenander and Rosenblatt's (1957) (G-R) classical result is used to judge the asymptotic efficiency of regression coefficients on deterministic regressors satisfying Grenander's condition. Without this condition, however, it is not obvious that the model is efficient. In this paper, we introduce such a model by proving the efficiency of the model with a slowly varying (SV) regressor under the same condition on error terms constrained in G-R. This kind of regressor is known to display asymptotic singularity in the sample moment matrices, as in Phillips (2007), such that Grenander's condition fails.

Higgs Production in Two-Photon Process and Transition Form Factor

The Higgs production in the two-photon fusion process is investigated where one of the photons is off-shell while the other one is on-shell. This process is realized in either electron-positron collision or electron-photon collision where the scattered electron or positron is detected (single tagging) and described by the transition form factor. We calculate the contributions to the transition form factor of the Higgs boson coming from top-quark loops and W-boson loops. We then study the $Q^2$ dependence of each contribution to the total transition form factor and also of the differential cross section for the Higgs production.Comment: 4pages, 6figur

Discovering the Network Granger Causality in Large Vector Autoregressive Models

This paper proposes novel inferential procedures for the network Granger causality in high-dimensional vector autoregressive models. In particular, we offer two multiple testing procedures designed to control discovered networks' false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics constructed by the debiased lasso estimator. The second procedure is based on the bootstrap distributions of the $t$-statistics made by imposing the null hypotheses. Their theoretical properties, including FDR control and power guarantee, are investigated. The finite sample evidence suggests that both procedures can successfully control the FDR while maintaining high power. Finally, the proposed methods are applied to discovering the network Granger causality in a large number of macroeconomic variables and regional house prices in the UK

Statistical Inference in High-Dimensional Generalized Linear Models with Asymmetric Link Functions

We have developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a pioneering method has been developed for logistic regression, which is a specific instance of GLMs, its direct applicability to other GLMs remains limited. In this study, we address this limitation by developing a new inference method designed for a class of GLMs with asymmetric link functions. More precisely, we first introduce a novel convex loss-based estimator and its associated system, which are essential components for the inference. We next devise a methodology for identifying parameters of the system required within the method. Consequently, we construct confidence intervals for GLMs in the high-dimensional regime. We prove that our proposal has desirable theoretical properties, such as strong consistency and exact coverage probability. Finally, we confirm the validity in experiments.Comment: 25 page

Penalized Likelihood Estimation in High-Dimensional Time Series Models

Open House, ISM in Tachikawa, 2014.6.13統計数理研究所オープンハウス（立川）、H26.6.13ポスター発

Estimation of Weak Factor Models

Last updated: 6/20/201