184 research outputs found

    A unified framework for solving a general class of conditional and robust set-membership estimation problems

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    In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

    Model comparison with Sharpe ratios

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    We show how to conduct asymptotically valid tests of model comparison when the extent of model mispricing is gauged by the squared Sharpe ratio improvement measure. This is equivalent to ranking models on their maximum Sharpe ratios, effectively extending the Gibbons, Ross, and Shanken (1989) test to accommodate the comparison of nonnested models. Mimicking portfolios can be substituted for any nontraded model factors, and estimation error in the portfolio weights is taken into account in the statistical inference. A variant of the Fama and French (2018) 6-factor model, with a monthly updated version of the usual value spread, emerges as the dominant model

    Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information

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    This paper considers identification and estimation of a nonparametric regression model with an unobserved discrete covariate. The sample consists of a dependent variable and a set of covariates, one of which is discrete and arbitrarily correlates with the unobserved covariate. The observed discrete covariate has the same support as the unobserved covariate, and can be interpreted as a proxy or mismeasure of the unobserved one, but with a nonclassical measurement error that has an unknown distribution. We obtain nonparametric identification of the model given monotonicity of the regression function and a rank condition that is directly testable given the data. Our identification strategy does not require additional sample information, such as instrumental variables or a secondary sample. We then estimate the model via the method of sieve maximum likelihood, and provide root-n asymptotic normality and semiparametric efficiency of smooth functionals of interest. Two small simulations are presented to illustrate the identification and the estimation results.

    Empirical cross-sectional asset pricing: a survey

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    I review the state of empirical asset pricing devoted to understanding cross-sectional differences in average rates of return. Both methodologies and empirical evidence are surveyed. Tremendous progress has been made in understanding return patterns. At the same time, there is a need to synthesize the huge amount of collected evidenc

    The Cross-Sectional Determinants of Returns: Evidence from Emerging Markets' Stocks

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    This paper looks at the cross-section of stock returns for the particular case of emerging markets. For each of 21 emerging markets I investigate the role of a set of a priori specified factors in the cross-section of returns, and subsequently assess whether the important factors are common. I use data on emerging markets’ individual stocks from the Emerging Markets Data Base (IFC). My results indicate that the most important pricing factors are common to the emerging markets in my sample, and that these important factors are similar to those identified for mature markets. Among the top six factors are technical factors and price level attributes. The payoffs to these factors are not correlated suggesting that even if investors across markets elect similar factors to price assets, premia are local.International Asset Pricing; Emerging Markets

    Improvements to PLSc: Remaining problems and simple solutions

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    The recent article by Dijkstra and Henseler (2015b) presents a consistent partial least squares (PLSc) estimator that corrects for measurement error attenuation and provides evidence showing that, generally, PLSc performs comparably to a wide variety of more conventional estimators for structural equation models (SEM) with latent variables. However, PLSc does not adjust for other limitations of conventional PLS, namely: (1) bias in estimates of regression coefficients due to capitalization on chance; and (2) overestimation of composite reliability due to the proportionality relation between factor loadings and indicator weights. In this article, we illustrate these problems and then propose a simple solution: the use of unit-weighted composites, rather than those constructed from PLS results, combined with errors-in-variables regression (EIV) by using reliabilities obtained from factor analysis. Our simulations show that these two improvements perform as well as or better than PLSc. We also provide examples of how our proposed estimator can be easily implemented in various proprietary and open source software packages

    Study on the Converted Total Least Squares method and its application in coordinate transformation

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    This thesis gives a brief introduction to Total Least Squares (TLS) comparing with the classical LS, and its common solutions by singular value decomposition (SVD) approaches and the iteration, also following with the advantages and disadvantages of both methods. One method named Converted Total Least Squares (CTLS) dealing with the errors-in-variables (EIV) model can solve the problems of both. The basic idea of it is to take the stochastic design matrix elements as virtual observations, and the TLS problem can be transformed into a LS problem. The significance of CTLS lies not merely in attaining the optimal estimation of parameters and more importantly in completing the theory of TLS with classical LS. As a comparison, another estimation method based on Partial-EIV model will also be presented, which can deal with the TLS problems with iterative algorithm. The coordinate transformation parameter estimation formula of both algorithms are derived. By specifying the accuracy assessment formulas of CTLS, this thesis identifies rigorously the degree of freedom of the EIV model in theory and solves the bottleneck problem of TLS that restricts the application and development of TLS

    Factor models, risk management and investment decisions

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    The recent extending empirical evidence regarding the power of factor models versus the traditional CAPM has motivated the research in the current thesis. Substantial controversy has been raised over two issues: 1) Are the new factors, market value and book-to-market equity, the most important sources of risk? and 2) Is it time to consider CAPM as a useless model? Effectively, these are the main questions we attempt to address in the current research within a unified framework of firm attributes and more aspects of the econometrical applied approaches. The main findings of the empirical research in this thesis show that, firstly the beta portfolio returns exhibit the highest volatility, confirming thus the beta as the most significant risk source. Secondly, the market portfolio absorbs the excess returns of the majority of value-weighted factor portfolios which is partly attributed to the mitigation of the January effect. In the seasonality area, we identify a strong October effect with high volatility but not high returns, a phenomenon that cannot be explained with a rational story. The re-examination of the Fama and French 1992 model with corrections of econometrical problems and the application of panel data methodology reveals that the sole significant factor over all the candidate variables is the price variable. Yet, even the power of the price factor is eliminating with the application of non-linear systems where the CAPM constraints are directly validated but with a negative sign. However, the presence of negative risk premium is consistent with the valid application of CAPM in a financial world where the occurrence of bad states of world is more frequent than the presence of up markets. Overall, the results of this thesis contribute to a thorough understanding of the factor models' performance which plays a key role in the financial investment decisions. The implication is that the CAPM should be still regarded as the basic financial model in the risk-return management process
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