77 research outputs found

    Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data

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    Much of the trading activity in Equity markets is directed to brokerage houses. In exchange they provide so-called "soft dollars," which basically are amounts spent in "research" for identifying profitable trading opportunities. Soft dollars represent about USD 1 out of every USD 10 paid in commissions. Obviously they are costly, and it is interesting for an institutional investor to determine whether soft dollar inputs are worth being used (and indirectly paid for) or not, from a statistical point of view. To address this question, we develop association measures between what broker--dealers predict and what markets realize. Our data are ordinal predictions by two broker--dealers and realized values on several markets, on the same ordinal scale. We develop a structural equation model with latent variables in an ordinal setting which allows us to test broker--dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. The method is then used to analyze our dataset.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS213 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    The Bivariate Normal Copula

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    We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

    Limited Information Estimation and Testing of Discretized Multivariate Normal Structural Models

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    (WP03/03 Clave pdf) We consider the estimation of multivariate normal structural models that have been discretized according to a set of thresholds. A popular estimation procedure for this restricted multinomial model consists in the following three stage estimator: First, estimate by maximum likelihood the thresholds for each variable separately from the univariate marginals of the contingency table. Then, estimate by maximum likelihood each of the polychoric correlations separately from the bivariate marginals of the contingency table given the estimated thresholds. Finally, if restrictions are imposed on the thresholds and polychoric correlations.Categorical data analysis, Data sparseness, GLS, Goodness of fit, Limited information estimation, LISREL, Paired comparisons data, Pseudo-maximun likelihood estimation, WLS estimation

    High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

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    Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43596/1/11336_2003_Article_1141.pd

    An Advance Study of Coveriance Structure

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    A Metropolis-Hastings Robbins-Monro Algorithm for Maximum Likelihood Nonlinear Latent Structure Analysis with a Comprehensive Measurement Model

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    A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm is proposed for maximum likelihood estimation in a general nonlinear latent structure model. The MH-RM algorithm represents a synthesis of the Markov chain Monte Carlo method, widely adopted in Bayesian statistics, and the Robbins-Monro stochastic approximation algorithm, well known in the optimization literature. The general latent structure model not only encompasses linear structural equations among latent variables, but also includes provisions for nonlinear latent regressions. Based on item response theory, a comprehensive measurement model provides the link between the latent structure and the observed variables. The MH-RM algorithm is shown to converge to a local maximum of the likelihood surface with probability one. Its significant advantages in terms of flexibility and efficiency over existing algorithms are illustrated with applications to real and simulated data. Implementation issues are discussed in detail. In addition, this dissertation integrates research on the parametrization and estimation of complex nonlinear latent variable models and furthers the understanding of the relationship between latent trait models and incomplete data estimation.Doctor of Philosoph

    The development of statistical theory in Britain, 1865-1925: a historical and sociological perspective

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    This thesis discusses the development of statistical theory in Britain in the period 1865 to 1925, and attempts to account for this development as an institutional and an intellectual phenomenon. Close connections are shown to have existed between statistical theory as a scientific specialty and eugenics and social Darwinism, in particular in the work of Francis Galton (1822 -1911) and Karl Pearson (1857- 1936). An analysis of eugenics as a social and political movement is presented, and it is argued that eugenics played a major role in facilitating the institutional growth of statistical theory as a field of study. Two scientific controversies involving Karl Pearson and his followers (with William Bateson and the early Mendelians, and with George Udny Yule) are examined, and it is suggested that these controversies might usefully be seen as generated and sustained by divergent social interests. The development of the theory of statistical inference in this period is discussed briefly, and the early pioneering work of W.S. Gosset ('Student') and R.A. Fisher is surveyed.It is concluded that the generation and assessment of scientific innovations by statisticians in this period must be seen as fundamentally affected by social factors having their origins both within science and in the wider society

    Estimation of polychoric correlation for misclassified polytomous variables.

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    Yiu Choi Fan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 69-71).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Estimation with Known Misclassification Probabilities --- p.7Chapter 2.1 --- Model --- p.7Chapter 2.2 --- Maximum Likelihood Estimation --- p.9Chapter 2.3 --- Standard Errors of the Parameter Estimates --- p.12Chapter 3 --- Numerical Examples (I) --- p.13Chapter 3.1 --- Analysis of Real Data --- p.13Chapter 3.2 --- Analysis of Artificial Data --- p.16Chapter 4 --- Simulation Study (I) --- p.19Chapter 4.1 --- Simulation Algorithm --- p.19Chapter 4.2 --- Simulation Design --- p.20Chapter 4.3 --- Reported Statistics --- p.21Chapter 4.4 --- Conclusions of Simulation Results --- p.22Chapter 5 --- Estimation by Double Sampling Scheme --- p.24Chapter 5.1 --- Introduction of Double Sampling Scheme --- p.24Chapter 5.2 --- Model --- p.25Chapter 5.3 --- Minimum Chi-square Estimation --- p.26Chapter 5.4 --- Statistical Properties of the Parameter Estimates --- p.28Chapter 6 --- Numerical Examples (II) --- p.30Chapter 6.1 --- "Analysis of Real Data, (2x2 Table)" --- p.30Chapter 6.2 --- Analysis of Artificial Data (3x3 Table) --- p.32Chapter 7 --- Simulation Study (II) --- p.34Chapter 7.1 --- Simulation Algorithm --- p.34Chapter 7.2 --- Simulation Design --- p.35Chapter 7.3 --- Reported Statistics --- p.37Chapter 7.4 --- Conclusions of Simulation Results --- p.38Chapter 8 --- Conclusions --- p.39Appendices --- p.42Chapter A.1 --- The proof of the expression for P(Zj = Ehk) --- p.42Chapter A.2 --- The proof of puv and whk{uv) --- p.44Chapter A.3 --- The proof of the covariance matrix Q --- p.47Chapter A.4 --- The proof of the matrix Σ --- p.52Tables A1-A9 --- p.54Tables B1-B6 --- p.63Bibliography --- p.6

    Is 'First in Family' a Good Indicator for Widening University Participation?

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    Universities use ‘first in family’ or ‘first generation’ as an indicator to increase the diversity of their student intake, but little is known about whether it is a good indicator of disadvantage. We use nationally representative, longitudinal survey data linked to administrative data from England to provide the first comprehensive analysis of this measure. We employ parametric probability (logit) and non-parametric classification (random forest) models to look at its relative predictive power of university participation and graduation. We find that being first in family is an important barrier to university participation and graduation, over and above other sources of disadvantage. This association seems to operate through the channel of early educational attainment. Our findings indicate that the first in family indicator could be key in efforts to widen participation at universities
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