Moving and Weighted Restriction of Estimates for Vanishing Curvature and Time Varying Bandwidth

Abstract

We study the nonparametric function estimation involving time series and change-point estimation. We show the cusum test for parameter changes in GARCH (1, 1), and time series models with cusum of squares test for variance change in nonstationary and nonparametric time series models. We also study the weak convergence of the sequential empirical processes of residuals in ARMA models. Endpoint and moving estimates for the circular maximal function, test with time varying bandwidth and for an oscillatory integral operator related to restriction to space curves are considered. We establish the application of bilinear approach to cone multipliers and restriction estimates for surface with curvatures of different signs. We discuss the Fourier and weighted restriction theorems for curves in 3R and space curves. Similarly we investigate the restriction theorems and estimates fora surface with negative curvature and some surfaces with vanishing curvatures.