1,837 research outputs found

    Robust Independent Component Analysis via Minimum Divergence Estimation

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    Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination and outliers. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the gamma-divergence due to its desirable property of super robustness, which gives the proposed method gamma-ICA. Statistical properties and technical conditions for the consistency of gamma-ICA are rigorously studied. In the limiting case, it leads to a necessary and sufficient condition for the consistency of MLE-ICA. This necessary and sufficient condition is weaker than the condition known in the literature. Since the parameter of interest in ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced to implement gamma-ICA. Furthermore, a data-driven selection for the gamma value, which is critical to the achievement of gamma-ICA, is developed. The performance, especially the robustness, of gamma-ICA in comparison with standard ICA methods is demonstrated through experimental studies using simulated data and image data.Comment: 7 figure

    Efficient and robust estimation for financial returns: an approach based on q-entropy

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    We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charv_at-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-o_ between robustness and e_ciency. The method is applied to expected re- turn and volatility estimation of _nancial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical re- sults on simulated and _nancial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothingq-entropy, robust estimation, power-divergence, _nancial returns

    Efficient and robust estimation for financial returns: an approach based on q-entropy

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    We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvàt-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and effciency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.q-entropy; robust estimation; power-divergence; financial returns

    2MTF VI. Measuring the velocity power spectrum

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    We present measurements of the velocity power spectrum and constraints on the growth rate of structure fσ8f\sigma_{8}, at redshift zero, using the peculiar motions of 2,062 galaxies in the completed 2MASS Tully-Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear Redshift Space Distortions (RSD), allowing us to recover unbiased fits down to scales k=0.2hMpc1k=0.2\,h\,{\rm Mpc}^{-1} without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of \cite{Watkins2015} is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations δm\delta m, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalise over this. We obtain \textit{scale-dependent} constraints on the growth rate of structure in two bins, finding fσ8=[0.550.13+0.16,0.400.17+0.16]f\sigma_{8} = [0.55^{+0.16}_{-0.13},0.40^{+0.16}_{-0.17}] in the ranges k=[0.0070.055,0.550.150]hMpc1k = [0.007-0.055, 0.55-0.150]\,h\,{\rm Mpc}^{-1}. We also find consistent results using four bins. Assuming scale-\textit{independence} we find a value fσ8=0.510.08+0.09f\sigma_{8} = 0.51^{+0.09}_{-0.08}, a 16%\sim16\% measurement of the growth rate. Performing a consistency check of General Relativity (GR) and combining our results with CMB data only we find γ=0.450.11+0.10\gamma = 0.45^{+0.10}_{-0.11}, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent fσ8f\sigma_{8} and γ0.55\gamma\approx0.55).Comment: 18 pages, 14 figures, 3 tables. Accepted for publication in MNRA

    Skew-normal shocks in the linear state space form DSGE model

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    Observed macroeconomic data – notably GDP growth rate, inflation and interest rates – can be, and usually are skewed. Economists attempt to fit models to data by matching first and second moments or co-moments, but skewness is usually neglected. It is so probably because skewness cannot appear in linear (or linearized) models with Gaussian shocks, and shocks are usually assumed to be Gaussian. Skewness requires non-linearities or non-Gaussian shocks. In this paper we introduce skewness into the DSGE framework assuming skewed normal distribution for shocks while keeping the model linear (or linearized). We argue that such a skewness can be perceived as structural, since it concerns the nature of structural shocks. Importantly, the skewed normal distribution nests the normal one, so that skewness is not assumed, but only allowed for. We derive elementary facts about skewness propagation in the state space model and, using the well-known Lubik-Schorfheide model, we run simulations to investigate how skewness propagates from shocks to observables in a standard DSGE model. We also assess properties of an ad hoc two-steps estimator of models’ parameters, shocks’ skewness parameters among them.
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