15,595 research outputs found
Adaptive goodness-of-fit tests based on signed ranks
Within the nonparametric regression model with unknown regression function
and independent, symmetric errors, a new multiscale signed rank statistic
is introduced and a conditional multiple test of the simple hypothesis
against a nonparametric alternative is proposed. This test is distribution-free
and exact for finite samples even in the heteroscedastic case. It adapts in a
certain sense to the unknown smoothness of the regression function under the
alternative, and it is uniformly consistent against alternatives whose sup-norm
tends to zero at the fastest possible rate. The test is shown to be
asymptotically optimal in two senses: It is rate-optimal adaptive against
H\"{o}lder classes. Furthermore, its relative asymptotic efficiency with
respect to an asymptotically minimax optimal test under sup-norm loss is close
to 1 in case of homoscedastic Gaussian errors within a broad range of
H\"{o}lder classes simultaneously.Comment: Published in at http://dx.doi.org/10.1214/009053607000000992 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Two Procedures for Robust Monitoring of Probability Distributions of Economic Data Streams induced by Depth Functions
Data streams (streaming data) consist of transiently observed, evolving in
time, multidimensional data sequences that challenge our computational and/or
inferential capabilities. In this paper we propose user friendly approaches for
robust monitoring of selected properties of unconditional and conditional
distribution of the stream basing on depth functions. Our proposals are robust
to a small fraction of outliers and/or inliers but sensitive to a regime change
of the stream at the same time. Their implementations are available in our free
R package DepthProc.Comment: Operations Research and Decisions, vol. 25, No. 1, 201
A comparative study of nonparametric methods for pattern recognition
The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
- …