Data Analysis Based On Monotonic Cubic Spline

Function estimation is a well-studied problem in nonparametric statistics,monotone functions arise frequently in econometrics and many other disciplines.Examples include demand and supply curve,fuctions relating the probability of firm insolvency to holding a risky assets and functions rep-resenting children's growth patterns through time,and so on.In many applications,the underlying function is believed to possess a qualitative property such as monotonicity,so that incorporating a monotonicity information into a estimation procedure can derive better result.In this paper,we estimate the underlying function using monotone cubic spline function.Firstly,we derive a order-restricted least squares estimate model,through the analysis of character of the monotone cubic spline function.Then we fit a monotone function by this method and find a reasonable value ofλ.The resulting estimated regression function is monotone in the whole domain and also has enough smoothness.It is very close to the theoretical function,which proves this method.Finally,we analyse a group of dose-response data by this method.