367 research outputs found
Modeling inequality and spread in multiple regression
We consider concepts and models for measuring inequality in the distribution
of resources with a focus on how inequality varies as a function of covariates.
Lorenz introduced a device for measuring inequality in the distribution of
income that indicates how much the incomes below the u quantile fall
short of the egalitarian situation where everyone has the same income. Gini
introduced a summary measure of inequality that is the average over u of the
difference between the Lorenz curve and its values in the egalitarian case.
More generally, measures of inequality are useful for other response variables
in addition to income, e.g. wealth, sales, dividends, taxes, market share and
test scores. In this paper we show that a generalized van Zwet type dispersion
ordering for distributions of positive random variables induces an ordering on
the Lorenz curve, the Gini coefficient and other measures of inequality. We use
this result and distributional orderings based on transformations of
distributions to motivate parametric and semiparametric models whose regression
coefficients measure effects of covariates on inequality. In particular, we
extend a parametric Pareto regression model to a flexible semiparametric
regression model and give partial likelihood estimates of the regression
coefficients and a baseline distribution that can be used to construct
estimates of the various conditional measures of inequality.Comment: Published at http://dx.doi.org/10.1214/074921706000000428 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Comparing Survival Curves Using Rank Tests
Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated
Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison
Testing of various classes of life distributions has been addressed in the
literature for more than 45 years. In this paper, we consider the problem of
testing exponentiality (which essentially implies no ageing) against positive
ageing which is captured by the fairly large class of new better than used in
expectation (NBUE) distributions. These tests of exponentiality against NBUE
alternatives are discussed and compared. The empirical size of the tests is
obtained by simulations. Power comparisons for different popular alternatives
are done using Monte Carlo simulations. These comparisons are made for both
small and large sample sizes. The paper concludes with a discussion in which
suggestions are made regarding the choices of the test when a particular
alternative is suspected
Beyond differences in means:robust graphical methods to compare two groups in neuroscience
If many changes are necessary to improve the quality of neuroscience research, one relatively
simple step could have great pay-offs: to promote the adoption of detailed graphical methods,
combined with robust inferential statistics. Here we illustrate how such methods can lead to a
much more detailed understanding of group differences than bar graphs and t-tests on means.
To complement the neuroscientistâs toolbox, we present two powerful tools that can help us
understand how groups of observations differ: the shift function and the difference asymmetry
function. These tools can be combined with detailed visualisations to provide complementary
perspectives about the data. We provide implementations in R and Matlab of the graphical
tools, and all the examples in the article can be reproduced using R scripts
Multi-Cause Degradation Path Model: A Case Study on Rubidium Lamp Degradation
At the core of satellite rubidium standard clocks is the rubidium lamp, which is a critical piece of equipment in a satellite navigation system. There are many challenges in understanding and improving the reliability of the rubidium lamp, including the extensive lifetime requirement and the dearth of samples available for destructive life tests. Experimenters rely on degradation experiments to assess the lifetime distribution of highly reliable products that seem unlikely to fail under the normal stress conditions, because degradation data can provide extra information about product reliability. Based on recent research on the rubidium lamp, this article presents a multiâcause degradation path model, including its application background, model description, modeling method, and parameter estimation method. Using the available data from degradation tests, we construct point estimates and interval estimates for rubidium lamp lifetimes using regression techniques
On boosting kernel regression
In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with L-2 boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast. and the variance diverges exponentially slow. The first boosting step is analysed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data
Partially linear censored quantile regression
Censored regression quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the explanatory covariates are assumed to act on the response through a non-linear function. Here the CRQ approach of Portnoy (J Am Stat Assoc 98:1001â1012, 2003) is extended to this partially linear setting. Basic consistency results are presented. A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on the Cox proportional hazards model and on methods not permitting nonlinearity
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
In this paper we propose a new nonparametric approach to interacting failing
systems (FS), that is systems whose probability of failure is not negligible in
a fixed time horizon, a typical example being firms and financial bonds. The
main purpose when studying a FS is to calculate the probability of default and
the distribution of the number of failures that may occur during the
observation period. A model used to study a failing system is defined default
model. In particular, we present a general recursive model constructed by the
means of inter- acting urns. After introducing the theoretical model and its
properties we show a first application to credit risk modeling, showing how to
assess the idiosyncratic probability of default of an obligor and the joint
probability of failure of a set of obligors in a portfolio of risks, that are
divided into reliability classes
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