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## Asymptotic Skewness in Exponential Family Nonlinear Models

CAVALCANTI, Alexsandro B.; CORDEIRO, Gauss M.; BOTTER, Denise A.; BARROSO, Lucia P.
Fonte: TAYLOR & FRANCIS INC Publicador: TAYLOR & FRANCIS INC
Tipo: Artigo de Revista Científica
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In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.; CAPES/Brazil; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP/Brazil; CNPq/Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

## A matrix formula for the skewness of maximum likelihood estimators

PATRIOTA, Alexandre G.; CORDEIRO, Gauss M.
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
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We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.; FAPESP; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPQ (Brazil)

## Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

LEMONTE, Artur J.; CORDEIRO, Gauss M.
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
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The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

## Reward skewness coding in the insula independent of probability and loss

Burke, Christopher J.; Tobler, Philippe N.
Fonte: American Physiological Society Publicador: American Physiological Society
Tipo: Artigo de Revista Científica
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Rewards in the natural environment are rarely predicted with complete certainty. Uncertainty relating to future rewards has typically been defined as the variance of the potential outcomes. However, the asymmetry of predicted reward distributions, known as skewness, constitutes a distinct but neuroscientifically underexplored risk term that may also have an impact on preference. By changing only reward magnitudes, we study skewness processing in equiprobable ternary lotteries involving only gains and constant probabilities, thus excluding probability distortion or loss aversion as mechanisms for skewness preference formation. We show that individual preferences are sensitive to not only the mean and variance but also to the skewness of predicted reward distributions. Using neuroimaging, we show that the insula, a structure previously implicated in the processing of reward-related uncertainty, responds to the skewness of predicted reward distributions. Some insula responses increased in a monotonic fashion with skewness (irrespective of individual skewness preferences), whereas others were similarly elevated to both negative and positive as opposed to no reward skew. These data support the notion that the asymmetry of reward distributions is processed in the brain and...

## Dissociable Influences of Skewness and Valence on Economic Choice and Neural Activity

Wright, Nicholas D.; Symmonds, Mkael; Morris, Laurel S.; Dolan, Raymond J.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
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Asymmetry in distributions of potential outcomes (i.e. skewness), and whether those potential outcomes reflect gains or losses (i.e. their valence), both exert a powerful influence on value-based choice. How valence affects the impact of skewness on choice is unknown. Here by orthogonally manipulating the skewness and valence of economic stimuli we show that both have an influence on choice. We show that the influence of skewness on choice is independent of valence, both across and within subjects. fMRI data revealed skew-related activity in bilateral anterior insula and dorsomedial prefrontal cortex, which shows no interaction with valence. Further, the expression of skew-related activity depends on an individual’s preference for skewness, and this was again independent of valence-related preference. Our findings highlight the importance of skewness in choice and show that its influence, both behaviourally and neurally, is distinct from an influence of valence.

## Sample Skewness as a Statistical Measurement of Neuronal Tuning Sharpness

Samonds, Jason M.; Potetz, Brian R.; Lee, Tai Sing
Tipo: Artigo de Revista Científica
Português
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We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested...

## Quadratic M-Estimators for ARCH-Type Processes

MEDDAHI, Nour; RENAULT, Éric
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 2257509 bytes; application/pdf
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This paper addresses the issue of estimating semiparametric time series models specified by their conditional mean and conditional variance. We stress the importance of using joint restrictions on the mean and variance. This leads us to take into account the covariance between the mean and the variance and the variance of the variance, that is, the skewness and kurtosis. We establish the direct links between the usual parametric estimation methods, namely, the QMLE, the GMM and the M-estimation. The ususal univariate QMLE is, under non-normality, less efficient than the optimal GMM estimator. However, the bivariate QMLE based on the dependent variable and its square is as efficient as the optimal GMM one. A Monte Carlo analysis confirms the relevance of our approach, in particular, the importance of skewness.; Cet article s’intéresse à l’estimation des modèles semiparamétriques de séries temporelles définis par leur moyenne et variance conditionnelles. Nous mettons en exergue l’importance de l’utilisation jointe des restrictions sur la moyenne et la variance. Ceci amène à tenir compte de la covariance entre la moyenne et la variance ainsi que de la variance de la variance, autrement dit la "skewness" et la "kurtosis". Nous établissons les liens directs entre les méthodes paramétriques usuelles d’estimation...

## Skewness risk and bond prices

RUGE-MURCIA, Francisco
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica
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Statistical evidence is reported that even outside disaster periods, agents face negative consumption skewness, as well as positive inflation skewness. Quantitative implications of skewness risk for nominal loan contracts in a pure exchange economy are derived. Key modeling assumptions are Epstein-Zin preferences for traders and asymmetric distributions for consumption and inflation innovations. The model is solved using a third-order perturbation and estimated by the simulated method of moments. Results show that skewness risk accounts for 6 to 7 percent of the risk premia depending on the bond maturity.

## Are Idiosyncratic Skewness and Idiosyncratic Kurtosis Priced?

Cao, Xu
Fonte: Brock University Publicador: Brock University
Tipo: Electronic Thesis or Dissertation
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This thesis investigates the pricing effects of idiosyncratic moments. We document that idiosyncratic moments, namely idiosyncratic skewness and idiosyncratic kurtosis vary over time. If a factor/characteristic is priced, it must show minimum variation to be correlated with stock returns. Moreover, we can identify two structural breaks in the time series of idiosyncratic kurtosis. Using a sample of US stocks traded on NYSE, AMEX and NASDAQ markets from January 1970 to December 2013, we run Fama-MacBeth test at the individual stock level. We document a negative and significant pricing effect of idiosyncratic skewness, consistent with the finding of Boyer et al. (2010). We also report that neither idiosyncratic volatility nor idiosyncratic kurtosis are consistently priced. We run robustness tests using different model specifications and period sub-samples. Our results are robust to the different factors and characteristics usually included in the Fama-MacBeth pricing tests. We also split first our sample using endogenously determined structural breaks. Second, we divide our sample into three equal sub-periods. The results are consistent with our main findings suggesting that expected returns of individual stocks are explained by idiosyncratic skewness. Both idiosyncratic volatility and idiosyncratic kurtosis are irrelevant to asset prices at the individual stock level. As an alternative method...

## Are Idiosyncratic Skewness and Idiosyncratic Kurtosis Priced?

Cao, Xu
Fonte: Brock University Publicador: Brock University
Tipo: Electronic Thesis or Dissertation
Português
Relevância na Pesquisa
37.343865%
This thesis investigates the pricing effects of idiosyncratic moments. We document that idiosyncratic moments, namely idiosyncratic skewness and idiosyncratic kurtosis vary over time. If a factor/characteristic is priced, it must show minimum variation to be correlated with stock returns. Moreover, we can identify two structural breaks in the time series of idiosyncratic kurtosis. Using a sample of US stocks traded on NYSE, AMEX and NASDAQ markets from January 1970 to December 2013, we run Fama-MacBeth test at the individual stock level. We document a negative and significant pricing effect of idiosyncratic skewness, consistent with the finding of Boyer et al. (2010). We also report that neither idiosyncratic volatility nor idiosyncratic kurtosis are consistently priced. We run robustness tests using different model specifications and period sub-samples. Our results are robust to the different factors and characteristics usually included in the Fama-MacBeth pricing tests. We also split first our sample using endogenously determined structural breaks. Second, we divide our sample into three equal sub-periods. The results are consistent with our main findings suggesting that expected returns of individual stocks are explained by idiosyncratic skewness. Both idiosyncratic volatility and idiosyncratic kurtosis are irrelevant to asset prices at the individual stock level. As an alternative method...

## The role of the SST-thermocline relationship in Indian Ocean Dipole skewness and its response to global warming

Ng, Benjamin; Cai, Wenju; Walsh, Kevin
Fonte: Nature Publishing Group Publicador: Nature Publishing Group
Tipo: Artigo de Revista Científica
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A positive Indian Ocean Dipole (IOD) tends to have stronger cold sea surface temperature anomalies (SSTAs) over the eastern Indian Ocean with greater impacts than warm SSTAs that occur during its negative phase. Two feedbacks have been suggested as the cause of positive IOD skewness, a positive Bjerknes feedback and a negative SST-cloud-radiation (SCR) feedback, but their relative importance is debated. Using inter-model statistics, we show that the most important process for IOD skewness is an asymmetry in the thermocline feedback, whereby SSTAs respond to thermocline depth anomalies more strongly during the positive phase than negative phase. This asymmetric thermocline feedback drives IOD skewness despite positive IODs receiving greater damping from the SCR feedback. In response to global warming, although the thermocline feedback strengthens, its asymmetry between positive and negative IODs weakens. This behaviour change explains the reduction in IOD skewness that many models display under global warming.

## Stationary State Skewness in KPZ Type Growth

Neergaard, John; Nijs, Marcel den
Tipo: Artigo de Revista Científica
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Stationary states in KPZ type growth have interesting short distance properties. We find that typically they are skewed and lack particle-hole symmetry. E.g., hill-tops are typically flatter than valley bottoms, and all odd moments of the height distribution function are non-zero. Stationary state skewness can be turned on and off in the 1+1 dimensional RSOS model. We construct the exact stationary state for its master equation in a 4 dimensional parameter space. In this state steps are completely uncorrelated. Familiar models such as the Kim-Kosterlitz model lie outside this space, and their stationary states are skewed. We demonstrate using finite size scaling that the skewness diverges with systems size, but such that the skewness operator is irrelevant in 1+1 dimensions, with an exponent $y_{sk}\simeq-1$, and that the KPZ fixed point lies at zero-skewness.; Comment: 29 pages, 4 figures, plain TeX

## A Bayesian estimate of the skewness of the Cosmic Microwave Background

Contaldi, C. R.; Ferreira, P. G.; Magueijo, J.; Gorski, K. M.
Tipo: Artigo de Revista Científica
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We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 year Cosmic Background Explorer (COBE) Differential Microwave Radiometer data. We find that the data is consistent with a Gaussian skewness, and with isotropy. Inclusion of non Gaussian degrees of freedom has essentially no effect on estimates of the power spectrum, if each $C_\ell$ is regarded as a separate parameter or if the angular power spectrum is parametrized in terms of an amplitude (Q) and spectral index (n). Fixing the value of the angular power spectrum at its maxiumum likelihood estimate, the best fit skewness is $S=6.5\pm6.0\times10^4(\muK)^3$; marginalizing over Q the estimate of the skewness is $S=6.5\pm8.4\times10^4(\muK)^3$ and marginalizing over n one has $S=6.5\pm8.5\times10^4(\muK)^3$.; Comment: submitted to Astrophysical Journal Letters

## The Process of price formation and the skewness of asset returns

Reimann, Stefan
Tipo: Artigo de Revista Científica
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Distributions of assets returns exhibit a slight skewness. In this note we show that our model of endogenous price formation \cite{Reimann2006} creates an asymmetric return distribution if the price dynamics are a process in which consecutive trading periods are dependent from each other in the sense that opening prices equal closing prices of the former trading period. The corresponding parameter $\alpha$ is estimated from daily prices from 01/01/1999 - 12/31/2004 for 9 large indices. For the S&P 500, the skewness distribution of all its constituting assets is also calculated. The skewness distribution due to our model is compared with the distribution of the empirical skewness values of the ingle assets.; Comment: 9 pages, 2 figures

## Skewness as a probe of Baryon Acoustic Oscillations

Juszkiewicz, Roman; Hellwing, Wojciech A.; van de Weygaert, Rien
Tipo: Artigo de Revista Científica
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In this study we show that the skewness S_3 of the cosmic density field contains a significant and potentially detectable and clean imprint of Baryonic Acoustic Oscillations. Although the BAO signal in the skewness has a lower amplitude than second order measures like the two-point correlation function and power spectrum, it has the advantage of a considerably lower sensitivity to systematic influences. Because it lacks a direct dependence on bias if this concerns simple linear bias, skewness will be considerably less beset by uncertainties due to galaxy bias. Also, it has a weaker sensitivity to redshift distortion effects. We use perturbation theory to evaluate the magnitude of the effect on the volume-average skewness, for various cosmological models. One important finding of our analysis is that the skewness BAO signal occurs at smaller scales than that in second order statistics. For an LCDM spectrum with WMAP7 normalization, the BAO feature has a maximum wiggle amplitude of ~3% and appears at a scale of ~82Mpc/h. We conclude that the detection of BAO wiggles in future extensive galaxy surveys via the skewness of the observed galaxy distribution may provide us with a useful, and potentially advantageous, measure of the nature of Dark Energy.; Comment: 7 pages...

## Variance and Skewness in the FIRST survey

Magliocchetti, M.; Maddox, S. J.; Lahav, O.; Wall, J. V.
Tipo: Artigo de Revista Científica
Português
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We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function (counts in cells). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function $w(\theta)$, the variance $\Psi_2$, and skewness $\Psi_3$ of the distribution for the various sub-samples chosen on different criteria. Both $w(\theta)$ and $\Psi_2$ show power-law behaviour with an amplitude corresponding a spatial correlation length of $r_0 \sim 10 h^{-1}$Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through $\Psi_3=S_3(\Psi_2)^{\alpha}$, with $\alpha=1.9\pm 0.1$, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and skewness are consistent with realistic models of galaxy clustering.; Comment: 13 pages, 21 inline figures, to appear in MNRAS

## Skewness as a Test of Non-Gaussian Primordial Density Fluctuations

Coles, P.; Moscardini, L.; Lucchin, F.; Matarrese, S.; Messina, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.21425%
We investigate the evolution of the skewness of the distribution of density fluctuations in CDM models with both Gaussian and non--Gaussian initial fluctuations. We show that the method proposed by Coles \& Frenk (1991), which uses the skewness of galaxy counts to test the hypothesis of Gaussian primordial density fluctuations, is a potentially powerful probe of initial conditions. As expected, the mass distribution in models with initially non--Gaussian fluctuations shows systematic departures from the Gaussian behaviour on intermediate to large scales. We investigate the effect of peculiar velocity distortions and normalisation upon the relationship between skewness and variance. These effects are generally small for the models we consider. Comparing our results to the QDOT measurements of the skewness, we find that our initially positive--skew models are clearly excluded by this analysis, but the available data do not rule out the negative--skew models.; Comment: 1+12 pages (in Latex), 3 figures available upon request, DAPD-202

## Computing the Skewness of the Phylogenetic Mean Pairwise Distance in Linear Time

Tsirogiannis, Constantinos; Sandel, Brody
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The phylogenetic Mean Pairwise Distance (MPD) is one of the most popular measures for computing the phylogenetic distance between a given group of species. More specifically, for a phylogenetic tree T and for a set of species R represented by a subset of the leaf nodes of T, the MPD of R is equal to the average cost of all possible simple paths in T that connect pairs of nodes in R. Among other phylogenetic measures, the MPD is used as a tool for deciding if the species of a given group R are closely related. To do this, it is important to compute not only the value of the MPD for this group but also the expectation, the variance, and the skewness of this metric. Although efficient algorithms have been developed for computing the expectation and the variance the MPD, there has been no approach so far for computing the skewness of this measure. In the present work we describe how to compute the skewness of the MPD on a tree T optimally, in Theta(n) time; here n is the size of the tree T. So far this is the first result that leads to an exact, let alone efficient, computation of the skewness for any popular phylogenetic distance measure. Moreover, we show how we can compute in Theta(n) time several interesting quantities in T that can be possibly used as building blocks for computing efficiently the skewness of other phylogenetic measures.; Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013)

## Detection of dark matter Skewness in the VIRMOS-DESCART survey: Implications for \Omega_0

Pen, Ue-Li; Zhang, Tongjie; van Waerbeke, Ludovic; Mellier, Yannick; Zhang, Pengjie; Dubinski, John
Tipo: Artigo de Revista Científica
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Weak gravitational lensing provides a direct statistical measure of the dark matter distribution. The variance is easiest to measure, which constrains the degenerate product \sigma_8\Omega^0.6. The degeneracy is broken by measuring the skewness arising from the fact that densities must remain positive, which is not possible when the initially symmetric perturbations become non-linear. Skewness measures the non-linear mass scale, which in combination with the variance measures \Omega directly. We present the first detection of dark matter skewness from the Virmos-Decart survey. We have measured the full three point function, and its projections onto windowed skewness. We separate the lensing mode and the B mode. The lensing skewness is detected for a compensated Gaussian on scales of 5.37 arc minutes to be \kappa^3=1.06+/-0.06x10^-6. The B-modes are consistent with zero at this scale. The variance for the same window function is \kappa^2= 5.32+/-0.62+/-0.98x10^-5, resulting in S_3=375^{+342}_{-124}. Comparing to N-body simulations, we find \Omega_0<0.5 at 90% confidence. The Canada-France-Hawaii-Telescope legacy survey and newer simulations should be able to improve significantly on the constraint.; Comment: 26 pages 8 figures, accepted by ApJ...

## Essays on Exchange Rate Risk

Rafferty, Barry John