2013 Volume 42 Issue 1 Pages 11-21
Varying coefficient, which might be varying on time, can be used for visualizations or interpretations of covariate effects. In general, varying coefficient is usually estimated by kernel smoothing method, which is essentially repetition of local multiple regression for data around the fixed time. Therefore, a pointwise confidence interval is constructed for varying coefficient. Recently, Satoh and Yanagihara (2010) developed statistical inference for linear varying coefficient. They proposed a simultaneous confidence interval for t ∈ R as a function of time. In this paper, we construct a simultaneous confidence interval for finite interval of time t ∈ [a, b] and improve an accuracy of confidence interval for varying coefficient. The proposed method can be applied for general regression model, and can be easily implemented by statistical software R. We compare the proposed confidence interval with that of Satoh and Yanagihara (2010) using longitudinal data in Potthoff and Roy (1964) and Watanabe et al. (1996).
