A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition

The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within homogeneous regions it ensures a similar behavior as non-adaptive smoothing (propagation), while avoiding smoothing among distinct regions (separation). In order to enable a proof of stability of estimates, the authors of the original study introduced an additional memory step aggregating the estimators of the successive iteration steps. Here, we study theoretical properties of the simplified algorithm, where the memory step is omitted. In particular, we introduce a new strategy for the choice of the adaptation parameter yielding propagation and stability for local constant functions with sharp discontinuities.Comment: 28 pages, 5 figure

Local Adaptive Grouped Regularization and its Oracle Properties for Varying Coefficient Regression

Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. While there are a number of methods for variable selection in a varying coefficient regression model, the existing methods are mostly for global selection, which includes or excludes each covariate over the entire domain. Presented here is a new local adaptive grouped regularization (LAGR) method for local variable selection in spatially varying coefficient linear and generalized linear regression. LAGR selects the covariates that are associated with the response at any point in space, and simultaneously estimates the coefficients of those covariates by tailoring the adaptive group Lasso toward a local regression model with locally linear coefficient estimates. Oracle properties of the proposed method are established under local linear regression and local generalized linear regression. The finite sample properties of LAGR are assessed in a simulation study and for illustration, the Boston housing price data set is analyzed.Comment: 30 pages, one technical appendix, two figure

Local polynomial modeling and bandwidth selection for time-varying linear models

This paper proposes a local polynomial modeling approach and bandwidth selection algorithm for estimating time-varying linear models (TVLM). The time-varying coefficients of a TVLM are modeled locally by polynomials and estimated using least-squares estimation with a kernel having a certain bandwidth or support. Asymptotic behavior of the proposed estimator is established and it shows that there exists an optimal local bandwidth which minimizes the weighted mean squared error (MSE). A data-driven variable bandwidth selection method is also proposed to estimate this optimal bandwidth. Simulation results show that the proposed LPM method with adaptive bandwidth selection outperforms conventional TVLM identification methods in a large variety of testing conditions. ©2009 IEEE.published_or_final_versionThe 7th International Conference on Information, Communications and Signal Processing (ICICS 2009), Macau, China, 8-10 December 2009. In Proceedings of the International Conference on Information, Communications and Signal Processing, 2009, p. 1-

Local polynomial modeling and bandwidth selection for time-varying linear models

This paper proposes a local polynomial modeling approach and bandwidth selection algorithm for estimating time-varying linear models (TVLM). The time-varying coefficients of a TVLM are modeled locally by polynomials and estimated using least-squares estimation with a kernel having a certain bandwidth or support. Asymptotic behavior of the proposed estimator is established and it shows that there exists an optimal local bandwidth which minimizes the weighted mean squared error (MSE). A data-driven variable bandwidth selection method is also proposed to estimate this optimal bandwidth. Simulation results show that the proposed LPM method with adaptive bandwidth selection outperforms conventional TVLM identification methods in a large variety of testing conditions. ©2009 IEEE.published_or_final_versionThe 7th International Conference on Information, Communications and Signal Processing (ICICS 2009), Macau, China, 8-10 December 2009. In Proceedings of the International Conference on Information, Communications and Signal Processing, 2009, p. 1-