1,720,959 research outputs found
Testing distributional equality for functional random variables
Full text linkIn this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space . First, we present a general recipe based on linear projections to construct a measure of dissimilarity between two probability distributions on . In particular, we consider a measure based on the energy statistic and present some of its nice theoretical properties. A plug-in estimator of this measure is used as the test statistic to construct a general two-sample test. Large sample distribution of this statistic is derived both under null and alternative hypotheses. However, since the quantiles of the limiting null distribution are analytically intractable, the test is calibrated using the permutation method. We prove the large sample consistency of the resulting permutation test under fairly general assumptions. We also study the efficiency of the proposed test by establishing a new local asymptotic normality result for functional random variables. Using that result, we derive the asymptotic distribution of the permuted test statistic and the asymptotic power of the permutation test under local contiguous alternatives. This establishes that the permutation test is statistically efficient in the Pitman sense. Extensive simulation studies are carried out and a real data set is analyzed to compare the performance of our proposed test with some state-of-the-art methods.Significant changes has been done from the previous versio
Some Nonparametric Tests for High-Dimensional and Functional Data
No full textThe advancement of information technology and sciences over the last few decades has facilitated the collection, storage and analysis of huge data sets. Many of these data sets contain observations having large number of features, and in some cases, this number is comparable to or even much larger than the sample size. Many traditional statistical methods cannot be meaningfully used in such situations. We develop some inferential tools for such high dimensional data. In particular, we consider the two-sample problem and the problem of testing spherical symmetry of a multivariate distributions. We construct some nonparametric tests in these contexts and investigate the limiting behavior of the proposed tests when the dimension diverges to infinity while the sample size may or may not grow with the dimension. Several simulated and real datasets are analyzed to compare their empirical performance with some state-of-the-art methods. In practice, we also encounter situations, where the feature are not scalar or finite-dimensional vectors, but they are functions or curves. We also focus on such functional data sets. We develop a two-sample test for functional data and construct a test for mutual independence among several random functions. Theoretical properties of our proposed tests are investigated under appropriate regularity conditions, and their empirical performance is evaluated by analyzing several simulated and real data sets against some state-of-the-art methods
Testing distributional equality for functional random variables
No full textIn this article, we present a nonparametric method for the general two-sample problem involving functional random variables modeled as elements of a separable Hilbert space H. First, we present a general recipe based on linear projections to construct a measure of dissimilarity between two probability distributions on H. In particular, we consider a measure based on the energy statistic and present some of its nice theoretical properties. A plug-in estimator of this measure is used as the test statistic to construct a general two-sample test. Large sample distribution of this statistic is derived both under null and alternative hypotheses. However, since the quantiles of the limiting null distribution are analytically intractable, the test is calibrated using the permutation method. We prove the large sample consistency of the resulting permutation test under fairly general assumptions. We also study the efficiency of the proposed test by establishing a new local asymptotic normality result for functional random variables. Using that result, we derive the asymptotic distribution of the permuted test statistic and the asymptotic power of the permutation test under local contiguous alternatives. This establishes that the permutation test is statistically efficient in the Pitman sense. Extensive simulation studies are carried out and a real data set is analyzed to compare the performance of our proposed test with some state-of-the-art methods
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
A consistent test of spherical symmetry for multivariate and high-dimensional data via data augmentation
Full text linkWe develop a test for spherical symmetry of a multivariate distribution
that works even when the dimension of the data is larger than the sample
size . We propose a non-negative measure such that
if and only if is spherically symmetric. We construct a consistent
estimator of using the data augmentation method and investigate its
large sample properties. The proposed test based on this estimator is
calibrated using a novel resampling algorithm. Our test controls the Type-I
error, and it is consistent against general alternatives. We also study its
behaviour for a sequence of alternatives , where
but , and . When
, for any , the power of our test converges to unity as
increases. However, if , the asymptotic power of our
test depends on . We establish this by proving the
minimax rate optimality of our test over a suitable class of alternatives and
showing that it is Pitman efficient when . Moreover,
our test is provably consistent for high-dimensional data even when is
larger than . Our numerical results amply demonstrate the superiority of the
proposed test over some state-of-the-art methods
- …
