1,508 research outputs found

    A State Dependent Regime Switching Model of Dynamic Correlations

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    Replaced with revised version of paper 07/29/09.dynamic correlations, regime switching, state dependent probabilities, thresholds, spillovers, Research Methods/ Statistical Methods,

    Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

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    An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.Comment: Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

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    Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1_1 penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Mixed membership stochastic blockmodels

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    Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.Comment: 46 pages, 14 figures, 3 table

    Negative volatility spillovers in the unrestricted ECCC-GARCH model

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    Copyright @ 2010 Cambridge University Press.This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories

    Inference on causal and structural parameters using many moment inequalities

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    This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by pp, is possibly much larger than the sample size nn. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters, a notable example is the market structure model of Ciliberto and Tamer (2009) where p=2m+1p=2^{m+1} with mm being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of pp Studentized (or tt-type) inequality-specific statistics, and analyze various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in nn while allowing for pp being much larger than nn, indeed pp can be of order exp⁥(nc)\exp (n^{c}) for some c>0c > 0. Importantly, all these results hold without any restriction on the correlation structure between pp Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.Comment: This paper was previously circulated under the title "Testing many moment inequalities

    The velocity distribution of nearby stars from Hipparcos data I. The significance of the moving groups

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    We present a three-dimensional reconstruction of the velocity distribution of nearby stars (<~ 100 pc) using a maximum likelihood density estimation technique applied to the two-dimensional tangential velocities of stars. The underlying distribution is modeled as a mixture of Gaussian components. The algorithm reconstructs the error-deconvolved distribution function, even when the individual stars have unique error and missing-data properties. We apply this technique to the tangential velocity measurements from a kinematically unbiased sample of 11,865 main sequence stars observed by the Hipparcos satellite. We explore various methods for validating the complexity of the resulting velocity distribution function, including criteria based on Bayesian model selection and how accurately our reconstruction predicts the radial velocities of a sample of stars from the Geneva-Copenhagen survey (GCS). Using this very conservative external validation test based on the GCS, we find that there is little evidence for structure in the distribution function beyond the moving groups established prior to the Hipparcos mission. This is in sharp contrast with internal tests performed here and in previous analyses, which point consistently to maximal structure in the velocity distribution. We quantify the information content of the radial velocity measurements and find that the mean amount of new information gained from a radial velocity measurement of a single star is significant. This argues for complementary radial velocity surveys to upcoming astrometric surveys

    MACROECONOMIC SHOCKS, HUMAN CAPITAL AND PRODUCTIVE EFFICIENCY: EVIDENCE FROM WEST AFRICAN FARMERS

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    Little empirical work has quantified the transitory effects of macroeconomic shocks on farm-level production behavior. We develop a simple analytical model to explain how macroeconomic shocks might temporarily divert managerial attention, thereby affecting farm-level productivity, but perhaps to different degrees and for different durations across production units. We then successfully test hypotheses from that model using panel data bracketing massive currency devaluation in the west African nation of Cote d'Ivoire. We find a transitory increase in mean plot-level technical inefficiency among Ivorien rice producers and considerable variation in the magnitude and persistence of this effect, attributable largely to ex ante complexity of operations, and the educational attainment and off-farm employment status of the plot manager.Labor and Human Capital, O1, Q12, Q18,
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