37 research outputs found
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 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 -statistics constructed by the debiased lasso estimator.
The second procedure is based on the bootstrap distributions of the
-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