Estimation and forecasting methodologies for nonparametric regression models via dynamic linear models

Nonparametric regression models have been used to explorefeatures of data. Various estimation procedures have been proposedfor estimating nonparametric regression models in the literature.The existing procedures may enjoy some statistically optimalproperties, but it is difficult to use the estimated regressionfunctions for the purpose of forecasting, i.e., prediction withindependent variables beyond the observed range. Motivated bydynamic linear model estimation and forecasting methodologiesdeveloped by citeA{west1997}, our research extends the study intwo directions by building connections between nonparametricregression models and dynamic linear models.First, for nonparametric regression models with independently andidentically distributed errors, we develop a regularizedregression spline to determine hyper-parameter values for errorsand compare estimation performance with a local linear estimator,a commonly used smoothing method for nonparametric regression.Second we study nonparametric regression models withautoregressive errors process since when collected over time, dataare likely to be serially correlated. From our simulation studies,the proposed methods outperform the local linear regression undercertain statistical settings for both models with i.i.d. andautoregressive error. Last, we establish a connection betweenvarying coefficient models and dynamic linear models.% what are "certain statistical settings" ?% with an autoregressive error process. We%provide some insights into the selection of hyper-parameter in the%varying coefficient models to save computing time.Both estimation and forecasting performances of the proposedmethod are examined via simulations. The proposed methods performwell for larger sample sizes. The proposed procedures aredemonstrated by analysis of two real data examples.