Spline-backfitted kernel smoothing of nonlinear additive autoregression model

Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the ``curse of dimensionality.'' Under rather weak conditions, we propose spline-backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high-dimensional time series, and theoretically reliable so inference can be made on the component functions with confidence. Simulation experiments have provided strong evidence that corroborates the asymptotic theory.Comment: Published in at http://dx.doi.org/10.1214/009053607000000488 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Oracally Efficient Two-Step Estimation of Generalized Additive Model

Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions. Our results are for weakly dependent data and we prove oracle efficiency. The SBK techniques is both computational expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Inference can be made on component functions based on asymptotic normality. Simulation evidence strongly corroborates with the asymptotic theory.Bandwidths, B spline, knots, link function, mixing, Nadaraya-Watson estimator

A Confidence Corridor for Sparse Longitudinal Data Curves

Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical side. Here we propose a method based on local linear smoothing that is implemented in the sparse (i.e., low number of nonzero coefficients) modelling situation. An SCC is constructed based on recent results obtained in applied probability theory. The precision and performance is demonstrated in a spectrum of simulations and applied to growth curve data. Technically speaking, our paper intensively uses recent insights into extreme value theory that are also employed to construct a shoal of confidence intervals (SCI).Longitudinal data, confidence band, Karhunen-Loève L² representation, local linear estimator, extreme value, double sum, strong approximation

Inclined Substrate Deposition of Nanostructured TiO2 Thin Films for DSSC Application

Nanostructured TiO2 films were deposited onto Indium Tin Oxide (ITO) and glass substrates by dc reactive magnetron sputtering at different substrate inclination angles. The structural and optical properties of the deposited films were studied by X-ray diffraction, scanning electron microscopy and UV-Vis spectrophotometer, respectively. Dye-sensitized solar cells (DSSC) were assembled using these TiO2 films as photoelectrodes and the effect of the substrate inclination angle in the preparing process of TiO2 films on the DSSC conversion efficiency was studied.info:eu-repo/semantics/publishedVersio

Estimation and Testing for Varying Coefficients in Additive Models with Marginal Integration

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (beta-mixing). Application of the test procedure to the West German real GNP data reveals that a partially linear varying coefficient model is best parsimonious in fitting the data dynamics, a fact that is also confirmed with residual diagnostics.adaptive volatility estimation, generalized hyperbolic distribution, value at risk, risk management

Derivative estimation and testing in generalized additive models

Estimation and testing procedures for generalized additive (interaction) model are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets

Nonparametric Estimation and Testing of Interaction in Additive Models

We consider an additive model with second order interaction terms. It is shown how the components of this model can be estimated using marginal integration, and the asymptotic distribution of the estimators is derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions are obtained, but in this case the asymptotics produce inaccurate results unless the number of observations is very large. For small or moderate sample sizes a bootstrap procedure is suggested and is shown to work well on a simulated example. Finally, our methods are illustrated on a five-dimensional production function for a set of Wisconsin farm data. In particular, the separability hypothesis for the production function is discussed

Distillation of Gaussian Einstein-Podolsky-Rosen steering with noiseless linear amplification

Einstein-Podolsky-Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. The inevitable loss and noise in the quantum channel will lead to decrease of the steerability and turn it from two-way to one-way. Despite an extensive research on protecting entanglement from decoherence, it remains a challenge to protect EPR steering due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering in lossy and noisy environment using measurement-based noiseless linear amplification. Our scheme recovers the two-way steerability from one-way in certain region of loss and enhances EPR steering for both directions. We also show that the distilled EPR steering allows to extract secret key in one-sided device-independent quantum key distribution. Our work paves the way for quantum communication exploiting EPR steering in practical quantum channels