Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation

Smoothing Categorical Data

Global models of a dataset reflect not only the large scale structure of the data distribution, they also reflect small(er) scale structure. Hence, if one wants to see the large scale structure, one should somehow subtract this smaller scale structure from the model. While for some kinds of model – such as boosted classifiers – it is easy to see the “important” components, for many kind of mode...

Gradient Based Smoothing Parameter Selection for Nonparametric Regression Estimation*

Data-driven bandwidth selection based on the gradient of an unknown regression function is considered. Uncovering gradients nonparametrically is of crucial importance across a broad range of economic environments such as determining risk premium or recovering distributions of individual preferences. The procedure developed here is shown to deliver bandwidths which have the optimal rate of conve...

Nonparametric regression for functional data: automatic smoothing parameter selection

We study regression estimation when the explanatory variable is functional. Nonparametric estimates of the regression operator have been recently introduced. They depend on a smoothing factor which controls its behavior, and the aim of our work is to construct some data-driven criterion for choosing this smoothing parameter. The criterion can be formulated in terms of a functional version of cr...

Review : Nonparametric Simple Regression : Smoothing Scatterplots

Nonparametric Renewal Function Estimation and Smoothing by Empirical Data

We consider an estimate of the renewal function (rf) using a limited number of independent observations of the interarrival times for an unknown interarrival-time distribution (itd). The nonparametric estimate is derived from the rf-representation as series of distribution functions (dfs) of consecutive arrival times using a finite summation and approximations of the latter by empirical dfs. Du...