L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Flexible generalized varying coefficient regression models

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition we give a general theorem that the problem of estimating the multivariate mean function is equivalent to that of estimating its univariate component functions. We discuss implications of the theorem for sieve and penalized least squares estimators, and then investigate the outcomes in full details for a kernel-type estimator. The kernel estimator is given as a solution of a system of nonlinear integral equations. We provide an iterative algorithm to solve the system of equations and discuss the theoretical properties of the estimator and the algorithm. Finally, we give simulation results.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1026 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Formulation and characterization of polyimide resilient foams of various densities for aircraft seating applications

Light weight, heat and fire resistant low smoke generating polyimide foams are developed for aircraft seating applications. The material is upgraded and classified into groups for fabrication of cushions possessing acceptable comfort properties. Refinement and selection of foaming processes using a variety of previously developd foaming techniques and definition of property relationships to arrive at the selection and classfication of polyimide foams into five groups in accordance with predetermined ILD values are emphasized

Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues

Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those estimators, when one or more of the true eigenvalues are tied. The $m$-out-of-$n$ bootstrap can be used to deal with problems of this general type, but it is very sensitive to the choice of $m$. In this paper we propose a new approach, where a tie diagnostic is used to determine the locations of ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is governed by a probability level, $\beta$, which in principle is an analogue of $m$ in the $m$-out-of-$n$ bootstrap. However, the tie-respecting bootstrap (TRB) is remarkably robust against the choice of $\beta$. This makes the TRB significantly more attractive than the $m$-out-of-$n$ bootstrap, where the value of $m$ has substantial influence on the final result. The TRB can be used very generally; for example, to test hypotheses about, or construct confidence regions for, the proportion of variability explained by a set of principal components. It is suitable for both finite-dimensional data and functional data.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ154 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Generalised additive dependency inflated models including aggregated covariates

Let us assume that X, Y and U are observed and that the conditional mean of U given X and Y can be expressed via an additive dependency of X, λ(X)Y and X + Y for some unspecified function . This structured regression model can be transferred to a hazard model or a density model when applied on some appropriate grid, and has important forecasting applications via structured marker dependent hazards models or structured density models including age-period-cohort relationships. The structured regression model is also important when the severity of the dependent variable has a complicated dependency on waiting times X, Y and the total waiting time X+Y . In case the conditional mean of U approximates a density, the regression model can be used to analyse the age-period-cohort model, also when exposure data are not available. In case the conditional mean of U approximates a marker dependent hazard, the regression model introduces new relevant age-period-cohort time scale interdependencies in understanding longevity. A direct use of the regression relationship introduced in this paper is the estimation of the severity of outstanding liabilities in non-life insurance companies. The technical approach taken is to use B-splines to capture the underlying one-dimensional unspecified functions. It is shown via finite sample simulation studies and an application for forecasting future asbestos related deaths in the UK that the B-spline approach works well in practice. Special consideration has been given to ensure identifiability of all models considered

High-dimensional Bell test for a continuous variable state in phase space and its robustness to detection inefficiency

We propose a scheme for testing high-dimensional Bell inequalities in phase space. High-dimensional Bell inequalities can be recast into the forms of a phase-space version using quasiprobability functions with the complex-valued order parameter. We investigate their violations for two-mode squeezed states while increasing the dimension of measurement outcomes, and finally show the robustness of high-dimensional tests to detection inefficiency.Comment: 8 pages, 2 figures; title and abstract changed, published versio