Spline Confidence Bands and Testing the Trend of Leaf Area Index of East Africa

Asymptotically exact and conservative confidence bands are obtained for the nonparametric regression function based on piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise nonparametric confidence interval of Huang(2003), the confidence bands are inflated only by a factor of sqrt{log(n)}, similar to the Nadaraya-Watson confidence bands of Hurdle(1989), and the local polynomial bands of Xia(1998) and Claeskens and Van Keilegom(2003). Simulation experiments have provided strong evidence that corroborates the asymptotic theory. Testing against the linear spline confidence band, the commonly used trigonometric trend is rejected with highly significant evidence for the Leaf Area Index of Aquatic Agriculture land, based on the remote sensing data collected from East Africa.