Asymptotic properties in partial linear models under dependence

Abstract

Bandwidth selection, kernel smoothing, mixing, partial linear models, 62G05, 62G20, 62M10,

Functional semiparametric partially linear model with autoregressive errors

“…We need to have the exact form of Φ n and an estimate of this matrix. As [1] pointed out, Φ n has ((n(n + 1)/2) − 1) different unknown parameters, but it is usual to assume that the elements in Φ n are functions of a k × 1 vector φ (k < n and remains constant as n increases). Then [13] the estimation of Φ n (φ) reduces to the estimation of φ.…”

“…In this context, Z is called a functional random variable. In a non-functional context, Aneiros and Quintela [1] considered the regression model 1], and ε i are unobserved dependent errors. They established the root-n-consistency of an estimator of β.…”

Truncated Estimator of Asymptotic Covariance Matrix in Partially Linear Models with Heteroscedastic Errors

“…Assume that {x i , t i , y i ; i = 1, · · · , n} satisfy model (1). Now we shall proceed to define a SLSE for the parametric component β by the nonparametric component g(·) approximated by a Bspline series.…”

“…x is | = O(1) and max 1≤i≤n g * (t i ) = O(n −1 k n ) + O(k −τ n ) it holds that J 2 = O(n −1 m 2 n ) · [O(n −1 k n ) + O(k −τ n )] 2 = o(1). By the definitions of β and αCov (γ − γ) = (W W ) −1 W ΩW (W W ) −1 ,where W = (X, B kn ).…”

Strong consistency of estimators in partially linear models for longitudinal data with mixing-dependent structure

“…Some limit theories can be found in the monograph of Lin and Lu [39]. Recently, the mixing-dependent error structure has also been used to study the nonparametric and semiparametric regression models, for instance, Roussas [40], Truong [41], Fraiman and Iribarren [42], Roussas and Tran [43], Masry and Fan [44], Aneiros and Quintela [45], and Fan and Yao [46].…”