Author
Vitaliana Rondonotti
Bio: Vitaliana Rondonotti is an academic researcher from European Central Bank. The author has contributed to research in topics: Smoothing & Goodness of fit. The author has an hindex of 3, co-authored 3 publications receiving 140 citations.
Topics: Smoothing, Goodness of fit, Autocovariance
Papers
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TL;DR: A new visualization is proposed, which shows the statistician the range of trade-offs that are available in SiZer, and demonstrates the effectiveness of the method.
Abstract: Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.
52 citations
TL;DR: In this paper, the authors developed SiZer-like ideas in time series analysis to address the important issue of significance of trends, which is not a straightforward extension, since one data set does not contain the information needed to distinguish "trend" from "dependence".
Abstract: Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are ‘really there’ and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish ‘trend’ from ‘dependence’. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.
46 citations
TL;DR: In this article, the authors extend SiZer to dependent data for the purpose of goodness-of-fit tests for time series models and show that such time series can have even more burstiness than is predicted by the popular, long-range dependent, Fractional Gaussian Noise model.
Abstract: In this paper, we extend SiZer (SIgnificant ZERo crossing of the derivatives) to dependent data for the purpose of goodness-of-fit tests for time series models. Dependent SiZer compares the observed data with a specific null model being tested by adjusting the statistical inference using an assumed autocovariance function. This new approach uses a SiZer type visualization to flag statistically significant differences between the data and a given null model. The power of this approach is demonstrated through some examples of time series of Internet traffic data. It is seen that such time series can have even more burstiness than is predicted by the popular, long- range dependent, Fractional Gaussian Noise model.
42 citations
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TL;DR: This work explores the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long-range dependence, and shows that much more than simple slope estimates are needed for detecting important traffic features.
115 citations
TL;DR: A simple factor method is proposed, based on bimodal kernels, to effectively deal with correlated data in the local polynomial regression framework and establish consistency of the estimator.
Abstract: We present a fully automated framework to estimate derivatives nonparametrically without estimating the regression function. Derivative estimation plays an important role in the exploration of structures in curves (jump detection and discontinuities), comparison of regression curves, analysis of human growth data, etc. Hence, the study of estimating derivatives is equally important as regression estimation itself. Via empirical derivatives we approximate the qth order derivative and create a new data set which can be smoothed by any nonparametric regression estimator. We derive L1 and L2 rates and establish consistency of the estimator. The new data sets created by this technique are no longer independent and identically distributed (i.i.d.) random variables anymore. As a consequence, automated model selection criteria (data-driven procedures) break down. Therefore, we propose a simple factor method, based on bimodal kernels, to effectively deal with correlated data in the local polynomial regression framework.
64 citations
TL;DR: A deep analysis of long-range dependence in a continually evolving Internet traffic mix by employing a number of recently developed statistical methods and found and analyzed several of the time series that exhibited more "bursty" characteristics than could be modeled as fractional Gaussian noise.
59 citations
TL;DR: A new visualization is proposed, which shows the statistician the range of trade-offs that are available in SiZer, and demonstrates the effectiveness of the method.
Abstract: Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.
52 citations
TL;DR: A graphical method based on SiZer (SIgnificant ZERo crossing of the differences) analysis, which is a scale-space visualization tool for statistical inferences, to find the differences between two curves that are present at each resolution level.
50 citations