Nonparametric Estimation Mothed Of Conditional Coefficient Of Variation

Conditional Coefficient of Variation has been often used in understanding the local variability of statistical data.In this paper : Under a general set-up which includes nonlinear time series model as a special case,we propose an efficient and adapative method for estimating the squared conditional coefficient of variation-local linear estimator,the MSE and MISE of the estimators are computed explicitly,and given out and proved the asymptotic normality of the estimators .The basic idea is to apply a local linear regressionto.We demonstrate that:without knowing the regression function ,we canestimate the squared conditional coefficient of variation asymptotically as well as if the regression function were given.This asymptotic result, established under the assumption that the observations are made from a strictly stationary and absolutely regular process,is also verified via simulation.Further,the asymptotic result paves the way for adapting an automatic bandwidth selection scheme. we consider regression model:Where (Y_i, X_i) be a two-dimensional strictly stationary process having the same marginal distribution as (Y, X),a sample of data (Y₁, X₁), (Y₂, X₂),... ,(Y_n, X_n) from an unknow joint f(·, ·).Letm(x) = E(Y|X = x) and 0 < σ² = Var(Y|X = x) < ∞. When the above model satisfies some conditions,we drive the main result of the paper:When regression function m(·) is know,Theorem 1: Suppose that model (1.0.1)and conditions (Cl)-(C4)hold ,if CV²(·)has a bounded second derivative.Then,when n →∞,h₁→0 and nh₁ → ∞, the estimator (*)...