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Stats, Volume 4, Issue 1

March 2021 - 16 articles

Cover Story: The Nadaraya–Watson kernel estimator is among the most popular non-parameteric regression techniques thanks to its simplicity. Its asymptotic bias was studied by Rosenblatt in 1969 and has been reported in several related works. However, its asymptotic nature gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making increases the need for hard guarantees. To alleviate this issue, a novel non-probabilistic upper bound of the bias is proposed, which relies on Lipschitz assumptions and mitigates some of Rosenblatt’s analysis prerequisites. The upper bound holds for a large class of kernels, designs, regression functions, admits finite bandwidths, and is tight even with large second derivatives of the regression function—where Rosenblatt’s analysis typically fails. View this paper
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Articles (16)

  • Article
  • Open Access
5 Citations
3,847 Views
12 Pages

17 March 2021

The testing of high-dimensional normality is an important issue and has been intensively studied in the literature, it depends on the variance–covariance matrix of the sample and numerous methods have been proposed to reduce its complexity. Principle...

  • Article
  • Open Access
2 Citations
2,094 Views
11 Pages

A Viable Approach to Mitigating Irreproducibility

  • David Trafimow,
  • Tonghui Wang and
  • Cong Wang

8 March 2021

In a recent article, Trafimow suggested the usefulness of imagining an ideal universe where the only difference between original and replication experiments is the operation of randomness. This contrasts with replication in the real universe where sy...

  • Article
  • Open Access
14 Citations
3,646 Views
22 Pages

4 March 2021

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count di...

  • Feature Paper
  • Article
  • Open Access
2 Citations
3,419 Views
21 Pages

An FDA-Based Approach for Clustering Elicited Expert Knowledge

  • Carlos Barrera-Causil,
  • Juan Carlos Correa,
  • Andrew Zamecnik,
  • Francisco Torres-Avilés and
  • Fernando Marmolejo-Ramos

4 March 2021

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian i...

  • Article
  • Open Access
2,734 Views
16 Pages

Assessment of Climate Change in Italy by Variants of Ordered Correspondence Analysis

  • Assuntina Cembalo,
  • Rosaria Lombardo,
  • Eric J. Beh,
  • Gianpaolo Romano,
  • Michele Ferrucci and
  • Francesca M. Pisano

1 March 2021

This paper explores climate changes in Italy over the last 30 years. The data come from the European observation gridded dataset and are concerned with the temperature throughout the country. We focus our attention on two Italian regions (Lombardy in...

  • Article
  • Open Access
2,305 Views
8 Pages

20 February 2021

In this paper, we present the Cumulative Median Estimation (CUMed) algorithm for robust sufficient dimension reduction. Compared with non-robust competitors, this algorithm performs better when there are outliers present in the data and comparably wh...

  • Article
  • Open Access
2 Citations
2,213 Views
16 Pages

13 February 2021

Dynamics of neural fields are tools used in neurosciences to understand the activities generated by large ensembles of neurons. They are also used in networks analysis and neuroinformatics in particular to model a continuum of neural networks. They a...

  • Article
  • Open Access
5 Citations
2,970 Views
20 Pages

4 February 2021

The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been p...

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Stats - ISSN 2571-905X