15,291 research outputs found

    Resistant estimates for high dimensional and functional data based on random projections

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    We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.Comment: 24 pages, 6 figure

    Resistant estimates for high dimensional and functional data based on random projections

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    We herein propose a new robust estimation method based on random projections that is adaptive and automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.Fil: Fraiman, Jacob Ricardo. Universidad de San Andrés; Argentina. Universidad de la República; Uruguay. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Svarc, Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentin

    Robust detail-preserving signal extraction

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    We discuss robust filtering procedures for signal extraction from noisy time series. Particular attention is paid to the preservation of relevant signal details like abrupt shifts. moving averages and running medians are widely used but have shortcomings when large spikes (outliers) or trends occur. Modifications like modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Better solutions can be based on robust regression techniques, which even work in real time because of increased computational power and faster algorithms. Reviewing previous work we present filters for robust signal extraction and discuss their merits for preserving trends, abrupt shifts and local extremes as well as for the removal of outliers. --

    Outlier robust corner-preserving methods for reconstructing noisy images

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    The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.Comment: Published at http://dx.doi.org/10.1214/009053606000001109 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Semiparametric Robust Estimation of Truncated and Censored Regression Models

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    Many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares (SCLS) are sensitive to outliers and data contamination as we document. Therefore, we propose a semipara- metric general trimmed estimator (GTE) of truncated and censored regression, which is highly robust and relatively imprecise. To improve its performance, we also propose data-adaptive and one-step trimmed estimators. We derive the robust and asymptotic properties of all proposed estimators and show that the one-step estimators (e.g., one-step SCLS) are as robust as GTE and are asymptotically equivalent to the original estimator (e.g., SCLS). The infinite-sample properties of existing and proposed estimators are studied by means of Monte Carlo simulations.Asymptotic normality;censored regression;one-step estimation;robust esti- mation;trimming;truncated regression

    Methods and algorithms for robust filtering

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    We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes. --Signal extraction,drift,edge,outlier,update algorithm

    Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

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    The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.asymptotic efficiency;binary-choice regression;breakdown point;maximum likelihood estimation;robust estimation;trimming

    CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles

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    Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation that does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. Utilizing the criterion from Regression Quantiles, and postulating a variety of dynamic updating processes we propose methods based on a Genetic Algorithm to estimate the unknown parameters of CAViaR models. We propose a Dynamic Quantile Test of model adequacy that tests the hypothesis that in each period the probability of exceeding the VaR must be independent of all the past information. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.
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