2,407 research outputs found

    On the convergence of Maronna's MM-estimators of scatter

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    In this paper, {we propose an alternative proof for the uniqueness} of Maronna's MM-estimator of scatter (Maronna, 1976) for NN vector observations y1,...,yN∈Rm\mathbf y_1,...,\mathbf y_N\in\mathbb R^m under a mild constraint of linear independence of any subset of mm of these vectors. This entails in particular almost sure uniqueness for random vectors yi\mathbf y_i with a density as long as N>mN>m. {This approach allows to establish further relations that demonstrate that a properly normalized Tyler's MM-estimator of scatter (Tyler, 1987) can be considered as a limit of Maronna's MM-estimator. More precisely, the contribution is to show that each MM-estimator converges towards a particular Tyler's MM-estimator.} These results find important implications in recent works on the large dimensional (random matrix) regime of robust MM-estimation

    Currency Total Return Swaps: Valuation and Risk Factor Analysis

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    Currency total return swaps (CTRS) are hybrid derivatives instruments that allow to simultaneously hedge against credit and currency risks. We develop a structural credit risk model to evaluate CTRS premia. Empirical test on a sample of 23,005 price observations from 59 underlying issuers yields an average percentage error of around 10%. This indicates that, beyond interest rate risk, firm-specific factors are major drivers of the variations in the valuation of these instruments. Regression analysis of residuals shows that exchange rate determinants account for up to 40% of model pricing errors – indicating that a currency risk premium affects the CTRS price significantly but only marginally, which confirms the prevalence of credit risk in the pricing of CTRS.Credit derivative, credit risk, currency risk

    Comfort and pressure profiles of two auto-adjustable positive airway pressure devices: a technical report

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    AbstractStudy objectives: The purpose of this study was to compare comfort parameters and pressure profiles of the AutoSetTM (Resmed) and the SOMNOsmartTM (Weinmann), two auto-adjustable positive airway pressure (APAP) devices. Setting: The sleep disorders center of a university hospital. Design: A single-blind randomized trial protocol was applied. A split night procedure allowed each patient to be treated in a crossover fashion with both APAP devices during one overnight study. Patients and methods: Fifty consecutive obstructive sleep apnea (OSA) patients were recruited. Each patient filled out an evaluation form for both devices after the study night. Visual analogue scales were used to score four comfort measures. Three CPAP outcomes generated by the devices (P50, P95 and Pmax) were assessed, compared with each other and correlated with the individually predicted CPAP (Ppred). Results: Forty-five males and 5 females, mean age 53.0 years, body mass index 31.0, were included. The mean apnea-hypopnea index was 58.7, the mean arousal index was 54.3. Mean CPAP-compliance before the titration study was 4.9h per night. Comparison of the two devices regarding the effect on the subjective sleep quality parameters showed no differences. The AutoSetTM pressure outcomes correlated significantly better with Ppred in comparison with the SOMNOsmartTM. The P50 and P95 but not the Pmax values were significantly lower in the SOMNOsmart™ as compared with the AutoSetTM (P50: 5.1±1.3 vs 7.1±1.9mbar, P<0.0001; P95: 7.8±3.0 vs 9.6±1.9mbar, P<0.0005; Pmax: 10.0±3.4 vs 10.8±1.8mbar, NS). Conclusion: While the subjective tolerance of the two APAP machines was comparable, these devices were characterized by different pressure profiles. The pressure parameters of the AutoSetTM correlated better with Ppred than those of the SOMNOsmartTM

    Convergence and Fluctuations of Regularized Tyler Estimators

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    This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a derivative of robust Tyler estimators, they inherit their robustness properties, notably their resilience to the presence of outliers. Nevertheless, one major problem that poses the use of RTEs in practice is represented by the question of setting the regularization parameter ρ\rho. While a high value of ρ\rho is likely to push all the eigenvalues away from zero, it comes at the cost of a larger bias with respect to the population covariance matrix. A deep understanding of the statistics of RTEs is essential to come up with appropriate choices for the regularization parameter. This is not an easy task and might be out of reach, unless one considers asymptotic regimes wherein the number of observations nn and/or their size NN increase together. First asymptotic results have recently been obtained under the assumption that NN and nn are large and commensurable. Interestingly, no results concerning the regime of nn going to infinity with NN fixed exist, even though the investigation of this assumption has usually predated the analysis of the most difficult NN and nn large case. This motivates our work. In particular, we prove in the present paper that the RTEs converge to a deterministic matrix when n→∞n\to\infty with NN fixed, which is expressed as a function of the theoretical covariance matrix. We also derive the fluctuations of the RTEs around this deterministic matrix and establish that these fluctuations converge in distribution to a multivariate Gaussian distribution with zero mean and a covariance depending on the population covariance and the parameter ρ\rho

    Relaxing order basis computation

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    International audienceThe computation of an order basis (also called sigma basis) is a fundamental tool for linear algebra with polynomial coefficients. Such a computation is one of the key ingredients to provide algorithms which reduce to polynomial matrices multiplication. This has been the case for column reduction or minimal nullspace basis of polynomial matrix over a field. In this poster, we are interested in the application of order basis to compute minimal matrix generators of a linear matrix sequence. In particular, we focus on the linear matrix sequence used in the Block Wiedemann algorithm

    Individuals tell a fascinating story: using unsupervised text mining methods to cluster policyholders based on their medical history

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    Background and objective: Classifying people according to their health profile is crucial in order to propose appropriate treatment. However, the medical diagnosis is sometimes not available. This is for example the case in health insurance, making the proposal of custom prevention plans difficult. When this is the case, an unsupervised clustering method is needed. This article aims to compare three different methods by adapting some text mining methods to the field of health insurance. Also, a new clustering stability measure is proposed in order to compare the stability of the tested processes. Methods : Nonnegative Matrix Factorization, the word2vec method, and marginalized Stacked Denoising Autoencoders are used and compared in order to create a high-quality input for a clustering method. A self-organizing map is then used to obtain the final clustering. A real health insurance database is used in order to test the methods. Results: the marginalized Stacked Denoising Autoencoder outperforms the other methods both in stability and result quality with our data. Conclusions: The use of text mining methods offers several possibilities to understand the context of any medical act. On a medical database, the process could reveal unexpected correlation between treatment, and thus, pathology. Moreover, this kind of method could exploit the refund dates contained in the data, but the tested method using temporality, word2vec, still needs to be improved since the results, even if satisfying, are not as better as the one offered by other methods
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