88,456 research outputs found
Spatial Quantile Regression
In a number of applications, a crucial problem consists in describing and analyzing the influence of a vector Xi of covariates on some real-valued response variable Yi. In the present context, where the observations are made over a collection of sites, this study is more difficult, due to the complexity of the possible spatial dependence among the various sites. In this paper, instead of spatial mean regression, we thus consider the spatial quantile regression functions. Quantile regression has been considered in a spatial context. The main aim of this paper is to incorporate quantile regression and spatial econometric modeling. Substantial variation exists across quantiles, suggesting that ordinary regression is insufficient on its own. Quantile estimates of a spatial-lag model show considerable spatial dependence in the different parts of the distribution.W wielu zastosowaniach, podstawowym problemem jest opis i analiza wpływu wektora skorelowanych zmiennych objaśniających X na zmienna objaśnianą Y. W przypadku, gdy obserwacje badanych zmiennych są dodatkowo rozmieszczone przestrzennie, zadanie jest jeszcze trudniejsze, ponieważ mamy dodatkowe zależności, wynikające ze zmienności przestrzennej. W tej pracy, w miejsce przestrzennej regresji wykorzystującej średnią, rozpatrzymy przestrzenna regresję kwantylową. Regresja kwantylowa zostanie omówiona w przestrzennym kontekście. Głównym celem pracy jest wskazanie na możliwości powiązania metodologii regresji kwantylowej i ekonometrycznego modelowania przestrzennego. Dodatkowe zasoby informacji o zmienności otrzymujemy badając kwantyle, wychodząc poza tradycyjny opis klasycznej regresji. Estymacja kwantylowa w modelu przestrzennym uwydatnia zależności przestrzenne dla różnych fragmentów rozważanych rozkładów
Local Quantile Regression
Quantile regression is a technique to estimate conditional quantile curves.
It provides a comprehensive picture of a response contingent on explanatory
variables. In a flexible modeling framework, a specific form of the conditional
quantile curve is not a priori fixed. % Indeed, the majority of applications do
not per se require specific functional forms. This motivates a local parametric
rather than a global fixed model fitting approach. A nonparametric smoothing
estimator of the conditional quantile curve requires to balance between local
curvature and stochastic variability. In this paper, we suggest a local model
selection technique that provides an adaptive estimator of the conditional
quantile regression curve at each design point. Theoretical results claim that
the proposed adaptive procedure performs as good as an oracle which would
minimize the local estimation risk for the problem at hand. We illustrate the
performance of the procedure by an extensive simulation study and consider a
couple of applications: to tail dependence analysis for the Hong Kong stock
market and to analysis of the distributions of the risk factors of temperature
dynamics
Bayesian quantile regression
Recent work by Schennach (2005) has opened the way to a Bayesian treatment of quantile regression. Her method, called Bayesian exponentially tilted empirical likelihood (BETEL), provides a likelihood for data y subject only to a set of m moment conditions of the form Eg(y, ?) = 0 where ? is a k dimensional parameter of interest and k may be smaller, equal to or larger than m. The method may be thought of as construction of a likelihood supported on the n data points that is minimally informative, in the sense of maximum entropy, subject to the moment conditions.
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