AbstractEquivariant high-breakdown point regression estimates are computationally expensive, and the corresponding algorithms become unfeasible for moderately large number of regressors. One important advance to improve computational speed one such estimator is fast-LTS algorithm. This article proposes an analogous algorithm computing S-estimates. The new algorithm, that we call "fast-S", also based on a "local improvement" step resampling initial candidates. allows substantial reduction...

We introduce a new computer-intensive method to estimate the distribution of robust regression estimates. The basic idea behind our is bootstrap reweighted representation To obtain that asymptotically correct, we include auxiliary scale in Our computationally simple because for each sample only have solve linear system equations. weights use are decreasing functions absolute value residuals and hence outlying observations receive small weights. This results resistant presence outliers data....

We consider robust principal components analysis (PCA) based on multivariate MM estimators. first study the robustness and efficiency of these estimators, particularly in terms eigenvalues eigenvectors. then focus inference procedures a fast bootstrap for This method is an alternative to approach asymptotic distribution estimators can also be used assess stability components. A formal consistency proof given, its finite-sample performance investigated through simulations. illustrate use PCA...

Witten and Tibshirani (2010) proposed an algorithim to simultaneously find clusters select clustering variables, called sparse K-means (SK-means). SK-means is particularly useful when the dataset has a large fraction of noise variables (that is, without information separate clusters). works very well on clean complete data but cannot handle outliers nor missing data. To remedy these problems we introduce new robust algorithm implemented in R package RSKC. We demonstrate use our four...

Abstract We study the empirical size and power of some recently proposed tests for multivariate normality (MVN) compare them with existing proposals that performed best in previously published studies. show Royston's [Royston, J.P., 1983b, Some techniques assessing based on Shapiro-Wilk W. Applied Statistics, 32, 121–133.] extension to Shapiro Wilk [Shapiro, S.S., Wilk, M.B., 1965, An analysis variance test (complete samples). Biometrika, 52, 591–611.] is unable achieve nominal significance...

Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional observations. In this article, we propose new class of estimators for principal components based on robust scale estimators. For fixed dimension q, robustly estimate the q-dimensional linear space best prediction data, sense minimizing sum...

Yohai and Zamar's τ-estimators of regression have excellent statistical properties but are nevertheless rarely used in practice because a lack available software the general impression that difficult to approximate. We will show, however, computational difficulties approximating similar nature those more popular S-estimators. The main goal this article is compare an algorithm for based on random resampling with some alternative heuristic search algorithms. show former not only simpler, when...

Abstract We are interested in a class of unsupervised methods to detect possible disease outbreaks, that is, rapid increases the number cases particular deviate from pattern observed past. The motivating application for this article deals with detecting outbreaks using generalized additive models (GAMs) model weekly counts certain infectious diseases. can use distance between predicted and specific week determine whether an important departure has occurred. Unfortunately, approach may not...

In large-scale quantitative proteomic studies, scientists measure the abundance of thousands proteins from human proteome in search novel biomarkers for a given disease. Penalized regression estimators can be used to identify potential among large set molecular features measured. Yet, performance and statistical properties these depend on loss penalty functions define them. Motivated by real plasma study, we propose new class penalized robust based elastic net penalty, which tuned keep...

This paper is about S-estimation for penalized regression splines.Penalized splines are one of the currently most used methods smoothing noisy data.The estimation method fitting such a spline model mostly based on least squares methods, which known to be sensitive outlying observations.In real world applications, outliers quite commonly observed.There several robust taking observations into account.We define and study S-estimators models.Hereby we replace by suitable method.By keeping...

Summary Preferential sampling in geostatistics occurs when the locations at which observations are made may depend on spatial process that underlines correlation structure of measurements. We show previously proposed Monte Carlo estimates for likelihood function not be approximating desired function. Furthermore, we argue that, preferential moderate complexity, alternative and widely available numerical methods to approximate produce better results than methods. illustrate our findings...

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) present a serious and sometimes hard-to-assess problem for large complex datasets. this paper we show small proportion of atypical observations have adverse effects on solutions found by sparse clustering algorithm Witten Tibshirani (2010). We propose robustification their...