A note on orthogonal series regression function estimators

Orthogonal samples for estimators in time series

Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some of these issues. For a broad class of statistics, an orthogonal sample is constructed through a slight modification of the original statistic, such that it s...

Consistency of orthogonal series density estimators based on grouped observations

The aim of this note is to indicate that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error (MISE) consistency when observations are grouped to the points of a uniform grid (prebinned). This kind of grouping is typical for computer rounding errors and may also be useful in data compression, before calculating estimates, e.g., using the FF...

A note on uniform consistency of monotone function estimators

A note on model selection in ( time series ) regression models -

The paper provides Monte Carlo evidence on the performance of general-to-specific and specific-to-general selection of explanatory variables in linear (auto)regressions. In small samples the former is markedly inefficient in terms of ex-ante forecasting performance.

Nonlinear Orthogonal Series Estimates for Randomdesign Regression

Let (X; Y) be a pair of random variables with supp(X) 0; 1] and EY 2 < 1. Let m be the corresponding regression function. Estimation of m from i.i.d. data is considered. The L 2 error with integration with respect to the design measure (i.e., the distribution of X) is used as an error criterion. Estimates are constructed by estimating the coeecients of an orthonormal expansion of the regression...