17,721 research outputs found
Multidimensional trimming based on projection depth
As estimators of location parameters, univariate trimmed means are well known
for their robustness and efficiency. They can serve as robust alternatives to
the sample mean while possessing high efficiencies at normal as well as
heavy-tailed models. This paper introduces multidimensional trimmed means based
on projection depth induced regions. Robustness of these depth trimmed means is
investigated in terms of the influence function and finite sample breakdown
point. The influence function captures the local robustness whereas the
breakdown point measures the global robustness of estimators. It is found that
the projection depth trimmed means are highly robust locally as well as
globally. Asymptotics of the depth trimmed means are investigated via those of
the directional radius of the depth induced regions. The strong consistency,
asymptotic representation and limiting distribution of the depth trimmed means
are obtained. Relative to the mean and other leading competitors, the depth
trimmed means are highly efficient at normal or symmetric models and
overwhelmingly more efficient when these models are contaminated. Simulation
studies confirm the validity of the asymptotic efficiency results at finite
samples.Comment: Published at http://dx.doi.org/10.1214/009053606000000713 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Towards an understanding of jet substructure
We present first analytic, resummed calculations of the rates at which
widespread jet substructure tools tag QCD jets. As well as considering
trimming, pruning and the mass-drop tagger, we introduce modified tools with
improved analytical and phenomenological behaviours. Most taggers have double
logarithmic resummed structures. The modified mass-drop tagger is special in
that it involves only single logarithms, and is free from a complex class of
terms known as non-global logarithms. The modification of pruning brings an
improved ability to discriminate between the different colour structures that
characterise signal and background. As we outline in an extensive
phenomenological discussion, these results provide valuable insight into the
performance of existing tools and help lay robust foundations for future
substructure studies.Comment: 52 pages, 18 figures. Version to be published in JHEP: added an
Appendix about Y-trimming and addressed several points raised by the refere
Network depth: identifying median and contours in complex networks
Centrality descriptors are widely used to rank nodes according to specific
concept(s) of importance. Despite the large number of centrality measures
available nowadays, it is still poorly understood how to identify the node
which can be considered as the `centre' of a complex network. In fact, this
problem corresponds to finding the median of a complex network. The median is a
non-parametric and robust estimator of the location parameter of a probability
distribution. In this work, we present the most natural generalisation of the
concept of median to the realm of complex networks, discussing its advantages
for defining the centre of the system and percentiles around that centre. To
this aim, we introduce a new statistical data depth and we apply it to networks
embedded in a geometric space induced by different metrics. The application of
our framework to empirical networks allows us to identify median nodes which
are socially or biologically relevant
Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models
Triangular systems with nonadditively separable unobserved heterogeneity
provide a theoretically appealing framework for the modelling of complex
structural relationships. However, they are not commonly used in practice due
to the need for exogenous variables with large support for identification, the
curse of dimensionality in estimation, and the lack of inferential tools. This
paper introduces two classes of semiparametric nonseparable triangular models
that address these limitations. They are based on distribution and quantile
regression modelling of the reduced form conditional distributions of the
endogenous variables. We show that average, distribution and quantile
structural functions are identified in these systems through a control function
approach that does not require a large support condition. We propose a
computationally attractive three-stage procedure to estimate the structural
functions where the first two stages consist of quantile or distribution
regressions. We provide asymptotic theory and uniform inference methods for
each stage. In particular, we derive functional central limit theorems and
bootstrap functional central limit theorems for the distribution regression
estimators of the structural functions. These results establish the validity of
the bootstrap for three-stage estimators of structural functions, and lead to
simple inference algorithms. We illustrate the implementation and applicability
of all our methods with numerical simulations and an empirical application to
demand analysis.Comment: 45 pages, 4 figures, 1 table, we have added grant funding
acknowledgement to v
Getting Institutions 'Right' for Whom: Credit Constraints and the Impact of Property Rights on the Quantity and Compostiton of Investment
The effects of property rights on investment are typically hypothesized to occur through a security-induced investment demand and a collateral-based credit supply. Using a two period model, this paper shows that for farms that are constrained in their access to liquidity, the investment demand effect will itself induce an increase in the endogenous shadow price of liquidity. Other things equal, this induced increase in the price of liquidity will discourage capital accumulation, and that the desired stock of expropriation-immune movable capital may decrease with tenure security. Empirical analysis of farm-level data from Paraguay corroborates this proposition and reveals that the underlying pattern of wealth-biased capital access creates a world in which property rights reform has differential effects across producer wealth classes and gets institutions "right" and agriculture moving for only for a wealthier subset of producers.
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