Algorithm 495: Solution of an Overdetermined System of Linear Equations in the Chebychev Norm [F4]

Barrodale, I.; Phillips, Chris

doi:10.1145/355644.355651

Cited by 152 publications

(75 citation statements)

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“…However, advocates of smooth adjustment (Teräsvirta, 1994;Dumas, 1994;Bertola and Caballero, 1990) suggest a Smooth Transition Autoregressive (STAR) model (Teräsvirta, 1994) as an appropriate formulation 3 . This model assumes no explicit threshold, rather the speed of RER mean reversion to its 2 In order to overcome the low power problem, other strands of the literature adopted long span studies or panel unit root studies in linear settings (Abuaf and Jorion, 1990;Lothian and Taylor, 1996;Taylor, 2002).…”

Section: Real Exchange Rate Issues and Related Literaturementioning

confidence: 99%

The behaviour of the real exchange rate: Evidence from regression quantiles

Nikolaou

2008

Journal of Banking & Finance

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Section: Real Exchange Rate Issues and Related Literaturementioning

confidence: 99%

The behaviour of the real exchange rate: Evidence from regression quantiles

Nikolaou

2008

Journal of Banking & Finance

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“…Numerical solutions to an in-sample meanexpected shortfall optimization were proposed, among others, by Rockafellar and Uryasev (2000), Bertsimas et al (2004), andBassett et al (2004). Generally, a sample analog of the mean-expected shortfall optimization can be reformulated as a linear program and solved efficiently with existing numerical algorithms, see Barrodale and Roberts (1974), D'Orey (1987), andPortnoy andKoenker (1997). The method can be generalized to 12 The spanning tests discussed in this subsection takes into account the estimation inaccuracy in the asset expected returns.…”

Section: Iid Sample Mean-crr Optimizationmentioning

confidence: 99%

“…This linear program can be solved very efficiently by classical simplex and interior point methods, see Barrodale and Roberts (1974) and Portnoy and Koenker (1997).…”

Section: Iid Sample Mean-crr Optimizationmentioning

confidence: 99%

Mean-Coherent Risk and Mean-Variance Approaches in Portfolio Selection: An Empirical Comparison

Polbennikov

Melenberg

2005

SSRN Journal

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We empirically analyze the implementation of coherent risk measures in portfolio selection. First, we compare optimal portfolios obtained through mean-coherent risk optimization with corresponding mean-variance portfolios. We find that, even for a typical portfolio of equities, the outcomes can be statistically and economically different. Furthermore, we apply spanning tests for the mean-coherent risk efficient frontiers, which we compare to their equivalents in the meanvariance framework. For portfolios of common stocks the outcomes of the spanning tests seem to be statistically the same.Keywords: portfolio choice, mean variance, mean coherent risk, comparison. JEL Classification: G11. I IntroductionThere is an ongoing debate in the financial literature on which risk measure to use in risk management and portfolio choice. As some risk measures are more theoretically appealing, others are easier to implement practically. For a long time, the standard deviation has been the predominant measure of risk in asset management. Mean-variance portfolio selection via quadratic optimization, introduced by Markowitz (1952), used to be the industry standard (see, for instance, Tucker et al. (1994)). Two justifications for using the standard deviation in portfolio choice can be given. First, an institution can view the standard deviation as a measure of risk, which needs to be minimized to limit the risk exposure. Second, a mean-variance portfolio maximizes expected utility of an investor if the utility index is quadratic or asset returns jointly follow an elliptically symmetric distribution. 1 Despite the computational advantages, the variance is not a satisfactory risk measure from the risk measurement perspective. First, mean-variance portfolios are not consistent with second-order stochastic dominance (SDD) and, thus, with the benchmark expected utility approach for portfolio selection. Second, but not independently, as a symmetric risk measure, the variance penalizes gains and losses in the same way. Artzner et al. (1999) give an axiomatic foundation for so-called coherent risk measures. They propose that a "rational" risk measure related to capital requirements 2 should be monotonic, subadditive, linearly homogeneous, and translation invariant. Tasche (2002) and Kusuoka (2001) demonstrate that a Choquet expectation with a concave distortion function represents a general class of coherent risk measures. Moreover, with some additional regularity restrictions, as imposed by Kusuoka (2001), the class of coherent risk measures becomes consistent with the second order stochastic dominance principle and thus generates portfolios consistent with the expected utility paradigm, see, for example, Ogryczak andRuszczyński (2002) andDe Giorgi (2005).The class of coherent risk measures generalizes expected shortfall, a co- Ingersoll (1987). 2 The capital requirements are relevant for asset management since they are directly applied to financial institutions, see the Basel Accord (1999).3 herent risk measure which received a...

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“…The prominent form of Quantile regression is the Median regression. Koenker is differentiable except at � � � � � � �� A simplex based algorithm was developed by Barrodale and Roberts [2] to solve the minimizer function and was later extended by Koenker and d'Orey [7] to Quantile regression estimation. The case where τ � �� corresponds to median regression, which is also known as L1 regression.…”

Section: Quantile Regressionmentioning

confidence: 99%

Cost Estimation Comparisons Between Least Square Regression and Quantile Regression on Fiber Reinforced Bridge Projects

Pamulaparthy¹,

Creese²,

GangaRao³

et al. 2016

IJEMME

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This paper focuses on the Least Square (LS) regression using the mean and Quantile (M) regression analysis using median which is based on "well-Known" parametric estimation methodologies. Data from Oregon and California highway bridges were used for the comparison of the two methods. Relationships were developed to predict the unit cost of FRP repair work and FRP cost was found to have a high degree of correlation with FRP area for both Oregon and California. It was observed that the Cost Estimating Relationships (CERs) obtained by Quantile (M) regression method had the smaller Mean Absolute Deviation (MAD) values and lower Mean Absolute Percentage Error (MAPE) values than Least Square (LS) regression. The stuudy showed that Quantile Regression is much less sensitive to outliers than Least Squares Regression.

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Algorithm 495: Solution of an Overdetermined System of Linear Equations in the Chebychev Norm [F4]

Cited by 152 publications

References 0 publications

The behaviour of the real exchange rate: Evidence from regression quantiles

The behaviour of the real exchange rate: Evidence from regression quantiles

Mean-Coherent Risk and Mean-Variance Approaches in Portfolio Selection: An Empirical Comparison

Cost Estimation Comparisons Between Least Square Regression and Quantile Regression on Fiber Reinforced Bridge Projects

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