47,091 research outputs found

    Estimation in semi-parametric regression with non-stationary regressors

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    In this paper, we consider a partially linear model of the form Yt=XtĻ„Īø0+g(Vt)+ĻµtY_t=X_t^{\tau}\theta_0+g(V_t)+\epsilon_t, t=1,...,nt=1,...,n, where {Vt}\{V_t\} is a Ī²\beta null recurrent Markov chain, {Xt}\{X_t\} is a sequence of either strictly stationary or non-stationary regressors and {Ļµt}\{\epsilon_t\} is a stationary sequence. We propose to estimate both Īø0\theta_0 and g(ā‹…)g(\cdot) by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of Īø0\theta_0 is still asymptotically normal with the same rate as for the case of stationary time series. In addition, we also establish an asymptotic distribution for the nonparametric estimator of the function g(ā‹…)g(\cdot). Some numerical examples are provided to show that our theory and estimation method work well in practice.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ344 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Corrections to holographic entanglement plateau

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    We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that Ī”S=S(L)āˆ’āˆ£S(Lāˆ’ā„“)āˆ’S(ā„“)āˆ£\Delta S=S(L)-|S(L-\ell)-S(\ell)| is nonnegative, where S(L)S(L) is the thermal entropy and S(Lāˆ’ā„“)S(L-\ell), S(ā„“)S(\ell) are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when ā„“ā‰¤ā„“c\ell \leq \ell_c the inequality saturates Ī”S=0\Delta S=0. In thermal AdS background, the holographic entanglement entropy leads to Ī”S=0\Delta S=0 for arbitrary ā„“\ell. We compute the next-to-leading order contributions to Ī”S\Delta S in the large central charge CFT at both high and low temperatures. In both cases we show that Ī”S\Delta S is strictly positive except for ā„“=0\ell = 0 or ā„“=L\ell = L. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.Comment: 32 pages, 8 figures; V2, typos corrected, published versio

    Measuring robustness of community structure in complex networks

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    The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, Ī³C\gamma_C, to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of Ī³C\gamma_C. The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1303.7434 by other author

    Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

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    A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A semiparametric profile likelihood approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the time trend function.cross-sectional dependence, nonlinear time trend, panel data, profile likelihood, semiparametric regression

    Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series

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    Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model and propose to estimate both alpha and g semiparametrically. We then show that the proposed estimator of alpha is still asymptotically normal with the same rate as for the case of stationary time series. We also establish the asymptotic normality for the nonparametric estimator of the function g and the uniform consistency of the nonparametric estimator. The simulated example is given to show that our theory and method work well in practice.asymptotic normality; beta-null recurrent Markov chain; consistency; kernel estimator; partially linear model
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