1,519 research outputs found
Modeling the variability of rankings
For better or for worse, rankings of institutions, such as universities,
schools and hospitals, play an important role today in conveying information
about relative performance. They inform policy decisions and budgets, and are
often reported in the media. While overall rankings can vary markedly over
relatively short time periods, it is not unusual to find that the ranks of a
small number of "highly performing" institutions remain fixed, even when the
data on which the rankings are based are extensively revised, and even when a
large number of new institutions are added to the competition. In the present
paper, we endeavor to model this phenomenon. In particular, we interpret as a
random variable the value of the attribute on which the ranking should ideally
be based. More precisely, if items are to be ranked then the true, but
unobserved, attributes are taken to be values of independent and
identically distributed variates. However, each attribute value is observed
only with noise, and via a sample of size roughly equal to , say. These
noisy approximations to the true attributes are the quantities that are
actually ranked. We show that, if the distribution of the true attributes is
light-tailed (e.g., normal or exponential) then the number of institutions
whose ranking is correct, even after recalculation using new data and even
after many new institutions are added, is essentially fixed. Formally, is
taken to be of order for any fixed , and the number of institutions
whose ranking is reliable depends very little on .Comment: Published in at http://dx.doi.org/10.1214/10-AOS794 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Using the bootstrap to quantify the authority of an empirical ranking
The bootstrap is a popular and convenient method for quantifying the
authority of an empirical ordering of attributes, for example of a ranking of
the performance of institutions or of the influence of genes on a response
variable. In the first of these examples, the number, , of quantities being
ordered is sometimes only moderate in size; in the second it can be very large,
often much greater than sample size. However, we show that in both types of
problem the conventional bootstrap can produce inconsistency. Moreover, the
standard -out-of- bootstrap estimator of the distribution of an empirical
rank may not converge in the usual sense; the estimator may converge in
distribution, but not in probability. Nevertheless, in many cases the bootstrap
correctly identifies the support of the asymptotic distribution of ranks. In
some contemporary problems, bootstrap prediction intervals for ranks are
particularly long, and in this context, we also quantify the accuracy of
bootstrap methods, showing that the standard bootstrap gets the order of
magnitude of the interval right, but not the constant multiplier of interval
length. The -out-of- bootstrap can improve performance and produce
statistical consistency, but it requires empirical choice of ; we suggest a
tuning solution to this problem. We show that in genomic examples, where it
might be expected that the standard, ``synchronous'' bootstrap will
successfully accommodate nonindependence of vector components, that approach
can produce misleading results. An ``independent component'' bootstrap can
overcome these difficulties, even in cases where components are not strictly
independent.Comment: Published in at http://dx.doi.org/10.1214/09-AOS699 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Feature selection when there are many influential features
Recent discussion of the success of feature selection methods has argued that
focusing on a relatively small number of features has been counterproductive.
Instead, it is suggested, the number of significant features can be in the
thousands or tens of thousands, rather than (as is commonly supposed at
present) approximately in the range from five to fifty. This change, in orders
of magnitude, in the number of influential features, necessitates alterations
to the way in which we choose features and to the manner in which the success
of feature selection is assessed. In this paper, we suggest a general approach
that is suited to cases where the number of relevant features is very large,
and we consider particular versions of the approach in detail. We propose ways
of measuring performance, and we study both theoretical and numerical
properties of the proposed methodology.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ536 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The distribution and excretion of insulin in man
A technique has been devised for performing
inulin clearances in man, which is a great
simplification on the method used by earlier workers.The simplification is threefold.A single injection is used in lieu of a large
priming injection followed by a sustained infusion
to maintain the blood inulin concentration. As a
result of this the blood concentration is constantly
falling throughout the experiment, so that
some difficulty may be experienced in getting the
exact mean blood concentration for each observation.Urine specimens were voided in the natural way,
and catherisation of the bladder followed by washing
out with saline was not practised. It was
felt that such a drastic procedure was not
warranted by a clinical experiment.This is an obvious source of error on account
of large differences between blood and urine
concentration, but if the urine flow is kept at
a high level by giving the subject large quantities
of water to drink this can be minimised.A marked improvement in the manner of
estimating blood inulin has been introduced.
This method is both simpler and of greater accuracy
than the original ones used in the estimation of
inulin. It is on account of the greater accuracy
that a relatively small single injection can be
used.This method is much simpler than a similar
one which has been introduced by Alving, Rubin and
Miller in America and which Is fairly generally
used in that country now. It is possible,
however,that their method may be of slightly
greater accuracy. I am sceptical of the
use of this method without removing the blood
glucose. The authors state that it is applicable
at blood concentrations of over 30 mg. /100 c.c.The colour due to fructose in Herbert's
method is 88% developed after 15 minutes, and
this follows a rectilinear relationship. At this
time the colour due to glucose is negligible. By
the other method, however, the specimens are
incubated for 1 hour, and though the proportions
of the reagents are different, one feels that there
must be a considerable colour development due to
glucose.The results obtained in a series of subjects
by this method are analysed and discussed, and
certain of the observations are compared with
synchronous urea clearances.In the course of these investigations the
distribution of inulin in the human body is also
studied, and the fact that inulin is excreted by
a simple physical process of filtration is
demonstrated by observations showing that the rate
of excretion increases proportionally to the blood
inulin concentration. As further proof of
filtration, it has also been shown that when the
fall of blood concentration is plotted logarithmically
against time, a rectilinear relationship
results
Hugh A. Barr to H. R. Miller (5 November)
News concerning Miller\u27s electionhttps://egrove.olemiss.edu/ciwar_corresp/1605/thumbnail.jp
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