Robust subsampling

… -AMERICAN MATHEMATICAL SOCIETY, 2001

Abstract. In Politis and Romano (1994) the subsampling methodology was put forth for approximating the sampling distribution (and the corresponding quantiles) of general statistics from iid and stationary data. In this note, we address the question of how well the subsampling distribution ...

2002

Les documents de travail ne reflètent pas la position de l'INSEE et n'engagent que leurs auteurs. Working papers do not reflect the position of INSEE but only the views of the authors.

Journal of Computational and Graphical Statistics, 1995

All known robust location and scale estimators with high breakdown point for multivariate sample's are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this work we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the estimator based on the Minimum Volume Ellipsoid, with the property that the number of subsamples required is substantially reduced with respect to the standard subsampling procedures used in both cases. We also discuss some bias and variability properties of the estimator obtained from the proposed subsampling process.

Journal of Econometrics, 1997

In this article, a general theory for the construction of confidence intervals or regions in the context of heteroskedastic-dependent data is presented. The basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data. This method was first proposed by Politis and Roman0 (1994b) for stationary observations. We extend their results to heteroskedastic observations, and prove a general asymptotic validity result under minimal conditions. In contrast, the usual bootstrap and mo?ing blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case-by-case zi+sis. Our general asymptotic results are applied to a regression setting with dependent heteroskedastic enors. 0 1997 Elsevier Science S.A.

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion how to estimate extreme order statistics with dependent data and present two applications to assessing financial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection.

1999

A general approach to constructing confidence intervals by subsampling was presented in Politis and Romano (1994). The crux of the method is recomputing a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method works under extremely weak conditions, it applies to independent, identically distributed (i.i.d.) observations as well as to dependent data situations, such as time series (possibly nonstationary), random fields, and marked point processes. In this article, we present some theorems showing: a new construction for confidence intervals that removes a previous condition, a general theorem showing the validity of subsampling for data-dependent choices of the block size, and a general theorem for the construction of hypothesis tests (not necessarily derived from a confidence interval construction). The arguments apply to both the i.i.d. setting and the dependent data case.

Statistica Sinica, 2018

We consider inference for the parameters of a linear model when the covariates are random and the relationship between response and covariates is possibly non-linear. Conventional inference methods such as z intervals perform poorly in these cases. We propose a double bootstrap-based calibrated percentile method, perc-cal, as a general-purpose CI method which performs very well relative to alternative methods in challenging situations * Lawrence D.

The Annals of Statistics, 2012

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions P. These results are then applied (i) to construct confidence regions that behave well uniformly over P in the sense that the coverage probability tends to at least the nominal level uniformly over P and (ii) to construct tests that behave well uniformly over P in the sense that the size tends to no greater than the nominal level uniformly over P. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and U-statistics.

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion how to estimate extreme order statistics with dependent data and present two applications to assessing nancial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection. JEL Classication: C14, C49, G11 Keywords: Resampling Methods, Extreme Value Statistics, Value at Risk, Portfolio Selection. INRA{CORELA, 65 Bd. de Brandebourg, 94205 Ivry/Seine, France. y Department of Economics, University of California at San Diego, La Jolla, CA 92093 USA. z Department of Mathematics, University of California at San Diego, La Jolla, CA 92093 USA. 1 Introduction Politis and Romano (1994) introduced the methodology of subsam...

Statistical Papers

Nowadays, in many different fields, massive data are available and for several reasons, it might be convenient to analyze just a subset of the data. The application of the D-optimality criterion can be helpful to optimally select a subsample of observations. However, it is well known that D-optimal support points lie on the boundary of the design space and if they go hand in hand with extreme response values, they can have a severe influence on the estimated linear model (leverage points with high influence). To overcome this problem, firstly, we propose a non-informative “exchange” procedure that enables us to select a “nearly” D-optimal subset of observations without high leverage values. Then, we provide an informative version of this exchange procedure, where besides high leverage points also the outliers in the responses (that are not necessarily associated to high leverage points) are avoided. This is possible because, unlike other design situations, in subsampling from big da...