Mathematical Sciences: Some Problems in Nonparametric Function Estimation

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Nonparametric function estimation is the representation of "noisy" data by a satisfactory smooth function without having to make restrictive assumptions about the function beforehand. The solution lies between artistically connecting all the data points and inadvertently smoothing out salient features of the data. This research will investigate possible definitions of the appropriate balance point between these extremes. Since many functions which differ only slightly may all appear to be satisfactory, definitions of boundaries for "satisfactory function" will also be sought. In addition, corrective techniques will be devised for technical problems with estimation using data near the boundaries of the observable (observed) values.