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##### Department of Mathematics, University of California San Diego

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## Nonparametric estimation of a regression curve

##### Abstract:

A regression function is a curve that describes the relation between two random variables $X$ and $Y$. For each value of the variable $X$, this curve reflects the average value taken by the variable $Y$. For example, $X$ might represent the height of individuals and $Y$ their weight, and the regression curve would give, for every possible value of the height, the average weight of individuals sharing that same height. In many real life applications, the regression curve that describes the relation between two given variables is unknown, but the value of ($X,Y$) is observed for a certain number of individuals. The unknown regression curve can then be estimated by finding the curve that fits well" the observed values of ($X,Y$). The estimated curve can be determined by parametric techniques, where we suppose that the curve is of a well specified type (for example we assume that the curve is a polynomial of order $3$ and we try to find the 3rd order polynomial that best fits the data). In this talk, we introduce nonparametric techniques of estimation, where no assumption is made on the shape of the curve. \vskip .1in \noindent Refreshments will be provided!

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### AP&M 2402

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