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Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data  [PDF]
Philippe Huber,Olivier Scaillet,Maria-Pia Victoria-Feser
Statistics , 2009, DOI: 10.1214/08-AOAS213
Abstract: 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.
A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses  [PDF]
Silvia Bacci,Francesco Bartolucci,Michela Gnaldi
Statistics , 2012,
Abstract: We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed approach, the random vector used to represent the latent traits is assumed to have a discrete distribution with support points corresponding to different latent classes in the population. We also allow for different parameterizations for the conditional distribution of the response variables given the latent traits - such as those adopted in the Graded Response model, in the Partial Credit model, and in the Rating Scale model - depending on both the type of link function and the constraints imposed on the item parameters. For the proposed models we outline how to perform maximum likelihood estimation via the Expectation-Maximization algorithm. Moreover, we suggest a strategy for model selection which is based on a series of steps consisting of selecting specific features, such as the number of latent dimensions, the number of latent classes, and the specific parametrization. In order to illustrate the proposed approach, we analyze data deriving from a study on anxiety and depression as perceived by oncological patients.
Bayesian Nonparametric Modeling for Multivariate Ordinal Regression  [PDF]
Maria DeYoreo,Athanasios Kottas
Statistics , 2014,
Abstract: Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate and multivariate ordinal regression, which is based on mixture modeling for the joint distribution of latent responses and covariates. The modeling framework enables highly flexible inference for ordinal regression relationships, avoiding assumptions of linearity or additivity in the covariate effects. In standard parametric ordinal regression models, computational challenges arise from identifiability constraints and estimation of parameters requiring nonstandard inferential techniques. A key feature of the nonparametric model is that it achieves inferential flexibility, while avoiding these difficulties. In particular, we establish full support of the nonparametric mixture model under fixed cut-off points that relate through discretization the latent continuous responses with the ordinal responses. The practical utility of the modeling approach is illustrated through application to two data sets from econometrics, an example involving regression relationships for ozone concentration, and a multirater agreement problem.
Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities  [PDF]
Albert Ferreiro-Castilla,Frederic Utzet
Mathematics , 2010,
Abstract: We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized Dirichlet series, which in turn is an infinite linear combination of exponential or Laplace densities. These results are applied to several examples.
The Poisson-exponential regression model under different latent activation schemes  [cached]
Francisco Louzada,Vicente G Cancho,Gladys D.C Barriga
Computational and Applied Mathematics , 2012, DOI: 10.1590/s1807-03022012000300010
Abstract: In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activationschemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer. Mathematical subject classification: 62N01, 62N99.
Non exponential relaxation in fully frustrated models  [PDF]
A. Fierro,A. de Candia,A. Coniglio
Physics , 1997, DOI: 10.1103/PhysRevE.56.4990
Abstract: We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.
Conditional entropy of ordinal patterns  [PDF]
Anton M. Unakafov,Karsten Keller
Mathematics , 2014, DOI: 10.1016/j.physd.2013.11.015
Abstract: In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern. We observe that this quantity provides a good estimation of the Kolmogorov-Sinai entropy in many cases. In particular, the conditional entropy of ordinal patterns of a finite order coincides with the Kolmogorov-Sinai entropy for periodic dynamics and for Markov shifts over a binary alphabet. Finally, the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real-world data.
Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”  [PDF]
Joachim Wuttke
Algorithms , 2012, DOI: 10.3390/a5040604
Abstract: The C library libkww provides functions to compute the Kohlrausch–Williams– Watts function, i.e., the Laplace–Fourier transform of the stretched (or compressed) exponential function exp(- t β ) for exponents β between 0.1 and 1.9 with double precision. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies, the numeric integration is enormously accelerated by using the Ooura–Mori double exponential transformation. The primitive of the cosine transform needed for the convolution integrals is also implemented. The software is hosted at http://apps.jcns.fz-juelich.de/kww; version 3.0 is deposited as supplementary material to this article.
Uniqueness of positive solutions of a $n$-Laplace equation in a ball in $\mathbb{r}^n$ with exponential nonlinearity  [PDF]
Adimurthi,Karthik A,Jacques Giacomoni
Mathematics , 2015,
Abstract: Let $n \geq 2$ and $\Omega \subset \mathbb{R}^n$ be a bounded domain. Then by Trudinger-Moser embedding, $W_0^{1,n}(\Omega)$ is embedded in an Orlicz space consisting of exponential functions. Consider the corresponding semi linear $n$-Laplace equation with critical or sub-critical exponential nonlinearity in a ball $B(R)$ with dirichlet boundary condition. In this paper, we prove that under suitable growth conditions on the nonlinearity, there exists an $\gamma_0 > 0$, and a corresponding $R_0(\gamma_0 ) > 0$ such that for all $0 < R < R_0$ , the problem admits a unique non degenerate positive radial solution $u$ with $\|u\|_{\infty}\geq \gamma_0$.
Transductive Ordinal Regression  [PDF]
Chun-Wei Seah,Ivor W. Tsang,Yew-Soon Ong
Computer Science , 2011, DOI: 10.1109/TNNLS.2012.2198240
Abstract: Ordinal regression is commonly formulated as a multi-class problem with ordinal constraints. The challenge of designing accurate classifiers for ordinal regression generally increases with the number of classes involved, due to the large number of labeled patterns that are needed. The availability of ordinal class labels, however, is often costly to calibrate or difficult to obtain. Unlabeled patterns, on the other hand, often exist in much greater abundance and are freely available. To take benefits from the abundance of unlabeled patterns, we present a novel transductive learning paradigm for ordinal regression in this paper, namely Transductive Ordinal Regression (TOR). The key challenge of the present study lies in the precise estimation of both the ordinal class label of the unlabeled data and the decision functions of the ordinal classes, simultaneously. The core elements of the proposed TOR include an objective function that caters to several commonly used loss functions casted in transductive settings, for general ordinal regression. A label swapping scheme that facilitates a strictly monotonic decrease in the objective function value is also introduced. Extensive numerical studies on commonly used benchmark datasets including the real world sentiment prediction problem are then presented to showcase the characteristics and efficacies of the proposed transductive ordinal regression. Further, comparisons to recent state-of-the-art ordinal regression methods demonstrate the introduced transductive learning paradigm for ordinal regression led to the robust and improved performance.
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