25 research outputs found
Efficient Estimation of an Additive Quantile Regression Model
In this paper two kernel-based nonparametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a viable alternative to the method of De Gooijer and Zerom (2003). With the aim to reduce variance of the first estimator, a second estimator is defined via sequential fitting of univariate local polynomial quantile smoothing for each additive component with the other additive components replaced by the corresponding estimates from the first estimator. The second estimator achieves oracle efficiency in the sense that each estimated additive component has the same variance as in the case when all other additive components were known. Asymptotic properties are derived for both estimators under dependent processes that are strictly stationary and absolutely regular. We also provide a demonstrative empirical application of additive quantile models to ambulance travel times.Additive models; Asymptotic properties; Dependent data; Internalized kernel smoothing; Local polynomial; Oracle efficiency
Estimating Generalized Additive Conditional Quantiles for Absolutely Regular Processes
We propose a nonparametric method for estimating the conditional quantile
function that admits a generalized additive specification with an unknown link
function. This model nests single-index, additive, and multiplicative quantile
regression models. Based on a full local linear polynomial expansion, we first
obtain the asymptotic representation for the proposed quantile estimator for
each additive component. Then, the link function is estimated by noting that it
corresponds to the conditional quantile function of a response variable given
the sum of all additive components. The observations are supposed to be a
sample from a strictly stationary and absolutely regular process. We provide
results on (uniform) consistency rates, second order asymptotic expansions and
point wise asymptotic normality of each proposed estimator
Efficient Estimation of an Additive Quantile Regression Model
In this paper two kernel-based nonparametric estimators are proposed for estimating the components
of an additive quantile regression model. The first estimator is a computationally convenient approach
which can be viewed as a viable alternative to the method of De Gooijer and Zerom (2003). With the aim
to reduce variance of the first estimator, a second estimator is defined via sequential fitting of univariate
local polynomial quantile smoothing for each additive component with the other additive components
replaced by the corresponding estimates from the first estimator. The second estimator achieves oracle
efficiency in the sense that each estimated additive component has the same variance as in the case when
all other additive components were known. Asymptotic properties are derived for both estimators under
dependent processes that are strictly stationary and absolutely regular. We also provide a demonstrative
empirical application of additive quantile models to ambulance travel times
Control4D: Dynamic Portrait Editing by Learning 4D GAN from 2D Diffusion-based Editor
Recent years have witnessed considerable achievements in editing images with
text instructions. When applying these editors to dynamic scene editing, the
new-style scene tends to be temporally inconsistent due to the frame-by-frame
nature of these 2D editors. To tackle this issue, we propose Control4D, a novel
approach for high-fidelity and temporally consistent 4D portrait editing.
Control4D is built upon an efficient 4D representation with a 2D
diffusion-based editor. Instead of using direct supervisions from the editor,
our method learns a 4D GAN from it and avoids the inconsistent supervision
signals. Specifically, we employ a discriminator to learn the generation
distribution based on the edited images and then update the generator with the
discrimination signals. For more stable training, multi-level information is
extracted from the edited images and used to facilitate the learning of the
generator. Experimental results show that Control4D surpasses previous
approaches and achieves more photo-realistic and consistent 4D editing
performances. The link to our project website is
https://control4darxiv.github.io.Comment: The link to our project website is https://control4darxiv.github.i
Approximations for moments of deĆæcit at ruin with exponential and subexponential claims
Abstract Consider a renewal insurance risk model with initial surplus u Āæ 0 and let A u denote the deĆæcit at the time of ruin. This paper investigates the asymptotic behavior of the moments of A u as u tends to inĆænity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the -moments of A u , where is a non-negative and non-decreasing function satisfying certain conditions
A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression
Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings
Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence
Under the condition that the observations, which come from a high-dimensional population (X,Y), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg minaIE(r(a,Y)|X=x), where the loss function r(a,y) is measurable. Furthermore, some related simulations are illustrated by using the cross validation method for both bivariate linear and bivariate nonlinear time series contaminated by heavy-tailed errors. The M-estimator is applied to a series of S&P 500 index futures andspot prices to compare its performance in practice with the "usual" squared-loss regression estimator.Asymptotic representation; Kernel function; Robust estimator; Strongly-mixing