Estimation Of The Varying Coefficient Model And The Semivarying Coefficient Model Under Different Data

Hastie and Tibshirani defined the varying coefficient model in 1993. It isdefined by the following linear model: Y=α^T(U)X+ε.where Y is the response variable, (U, X) is the associated covariates.εis therandom error, it is independent of (U, X) withEε=0, Var(ε)=σ².α(·)=(α₁(·),…,α_p(·))^T is a p_dimensional vector of unknowncoefficient functions.The varying coefficient models are used in wide applications.The semivarying coefficient model is generalization of the varying coefficientmodel. The present paper is discussed the model with structure: Y=α^T(U)X+β^TZ+ε.where Y is the response variable, (U,X,Z) is the associated covariates.εisthe random error, it is independent of (U, X, Z) withEε=0, Var(ε)=σ²Â·Î±(·)=(α₁(·),…,α_p(·))^T andβare respectively ap_dimensional vector of unknown coefficient functions and q_dimensionalvector by unknown parameters. In the paper, there are following three problems been studied:1). The estimates of the varying coefficient model with the correlated randomerrors are given. The local linear method is employed. The asymptoticalnormality of all estimators are discussed.2). Estimates of the semivarying coefficient model with the correlated randomerrors are given. The estimates of all function are got by the local linear method.The estimates of constants are got by the least squares method and theasymptotical normality of all estimators is discussed.3). By the local linear method the estimations of semivarying coefficient modelswith censored data are given and the asymptotical normality of constantestimators are discussed.