Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross-sectional resampling

Spatial autoregressive models typically rely on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix, although it is unknown in most empirical applications. Thus, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual nonzero connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide (Formula presented.) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably. © 2021 The Authors. Environmetrics published by John Wiley & Sons, Ltd

Estimation of the spatial weighting matrix for regular lattice data -- An adaptive lasso approach with cross-sectional resampling

Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide ($\mathrm{NO_2}$) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably

Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix W. However, in practice, the structure of W is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain W, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With W determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin

Observation of two new Ξb−\Xi_b^- baryon resonances

Two structures are observed close to the kinematic threshold in the $\Xi_b^0 \pi^-$ mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$ recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content $bds$ are expected in this mass region: the spin-parity $J^P = \frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ states, denoted $\Xi_b^{\prime -}$ and $\Xi_b^{*-}$. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be $m(\Xi_b^{\prime -}) - m(\Xi_b^0) - m(\pi^{-}) = 3.653 \pm 0.018 \pm 0.006$ MeV$/c^2$, $m(\Xi_b^{*-}) - m(\Xi_b^0) - m(\pi^{-}) = 23.96 \pm 0.12 \pm 0.06$ MeV$/c^2$, $\Gamma(\Xi_b^{*-}) = 1.65 \pm 0.31 \pm 0.10$ MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of $\Gamma(\Xi_b^{\prime -}) < 0.08$ MeV at 95% confidence level. Relative production rates of these states are also reported.Comment: 17 pages, 2 figure

Measurement of the mass and lifetime of the Ωb−\Omega_b^- baryon

A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\pm9$ $\Omega_b^-\to\Omega_c^0\pi^-$, $\Omega_c^0\to pK^-K^-\pi^+$ decays. Using the $\Xi_b^-\to\Xi_c^0\pi^-$, $\Xi_c^0\to pK^-K^-\pi^+$ decay mode for calibration, the lifetime ratio and absolute lifetime of the $\Omega_b^-$ baryon are measured to be \begin{align*} \frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\ \tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the uncertainties are statistical, systematic and from the calibration mode (for $\tau_{\Omega_b^-}$ only). A measurement is also made of the mass difference, $m_{\Omega_b^-}-m_{\Xi_b^-}$, and the corresponding $\Omega_b^-$ mass, which yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2. \end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-008.htm

Study of B−→DK−π+π−B^{-}\to DK^-\pi^+\pi^- and B−→Dπ−π+π−B^-\to D\pi^-\pi^+\pi^- decays and determination of the CKM angle γ\gamma

We report a study of the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp}\pi^{\pm}$ and CP-even $K^+K^-$ and $\pi^+\pi^-$ final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0~fb$^{-1}$. We observe the first significant signals in the CP-even final states of the $D$ meson for both the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^+\pi^-$ final state of the $B^-\to D\pi^-\pi^+\pi^-$ decay. Evidence for the ADS suppressed decay $B^{-}\to DK^-\pi^+\pi^-$, with $D\to K^+\pi^-$, is also presented. From the observed yields in the $B^-\to DK^-\pi^+\pi^-$, $B^-\to D\pi^-\pi^+\pi^-$ and their charge conjugate decay modes, we measure the value of the weak phase to be $\gamma=(74^{+20}_{-19})^{\rm o}$. This is one of the most precise single-measurement determinations of $\gamma$ to date.Comment: 22 pages, 9 figures; All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-020.htm

Study of Bc+B_c^+ decays to the K+K−π+K^+K^-\pi^+ final state and evidence for the decay Bc+→χc0π+B_c^+\to\chi_{c0}\pi^+

A study of $B_c^+\to K^+K^-\pi^+$ decays is performed for the first time using data corresponding to an integrated luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. Evidence for the decay $B_c^+\to\chi_{c0}(\to K^+K^-)\pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $\frac{\sigma(B_c^+)}{\sigma(B^+)}\times\mathcal{B}(B_c^+\to\chi_{c0}\pi^+)$ to be $(9.8^{+3.4}_{-3.0}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times 10^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma(B_c^+)$ and $\sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $\bar b c$ weak annihilation is found for the region $m(K^-\pi^+)<1.834\mathrm{\,Ge\kern -0.1em V\!/}c^2$, with a significance of 2.4 standard deviations.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-022.html, link to supplemental material inserted in the reference

Observation of J/ψpJ/\psi p resonances consistent with pentaquark states in Λb0→J/ψK−p{\Lambda_b^0\to J/\psi K^-p} decays

Observations of exotic structures in the $J/\psi p$ channel, that we refer to as pentaquark-charmonium states, in $\Lambda_b^0\to J/\psi K^- p$ decays are presented. The data sample corresponds to an integrated luminosity of 3/fb acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis is performed on the three-body final-state that reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the $J/\psi p$ mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of $4380\pm 8\pm 29$ MeV and a width of $205\pm 18\pm 86$ MeV, while the second is narrower, with a mass of $4449.8\pm 1.7\pm 2.5$ MeV and a width of $39\pm 5\pm 19$ MeV. The preferred $J^P$ assignments are of opposite parity, with one state having spin 3/2 and the other 5/2.Comment: 48 pages, 18 figures including the supplementary material, v2 after referee's comments, now 19 figure

Model-independent evidence for J/ψpJ/\psi p contributions to Λb0→J/ψpK−\Lambda_b^0\to J/\psi p K^- decays

The data sample of $\Lambda_b^0\to J/\psi p K^-$ decays acquired with the LHCb detector from 7 and 8~TeV $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$, is inspected for the presence of $J/\psi p$ or $J/\psi K^-$ contributions with minimal assumptions about $K^- p$ contributions. It is demonstrated at more than 9 standard deviations that $\Lambda_b^0\to J/\psi p K^-$ decays cannot be described with $K^- p$ contributions alone, and that $J/\psi p$ contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for $P_c^+\to J/\psi p$ charmonium-pentaquark states in the same data sample.Comment: 21 pages, 12 figures (including the supplemental section added at the end