smoother nonparametric nature smooth scatterplot smoothing categorical smoothing local averaging neighbourhoods around brand smoothing parameter fundamental tradeoff between bias and variance robustified infinitely smooth close symmetric nearest neighbourhood running mean nearest neighbourhood moving average smoother running lines smoother weighted least-squares loess kernel metric distance metric rank distance Hanning twicing regression smoothers linear degrees of freedom equivalent kernels linear equivalent kernel loess smooth equivalent degrees of freedom piecewise knots cubic splines number when the knots are given natural cubic spline effective dimension sorted values natural-spline basis local averaging kernel loess tri-cube weight span loess nearest neighbours Nearest thin-plate spline tensor product per~se Updating formula for running-line smooth Basis for natural splines Derivation of smoothing splines Semi-parametric regression estimating equations Efficient kernel smoothing smoothing splines running mean target point interior knots smoothing parameter running-lines smooth equivalent kernels equivalent kernel basis functions running-lines smoother least-squares line kernel smoothers kernel smoother cubic smoothing spline target value symmetric nearest neighbourhood spaced data scatterplot smoother rigid form nearest neighbours nearest neighbourhood natural splines locally-weighted running-lines kernel smooth weighted least-squares fit weight function unweighted running-lines smoother time series symmetric nearest neighbours symmetric nearest neighbourhoods standard Gaussian density single predictor scatterplot smoothing scatterplot smoothers scatterplot smooth predictor space piecewise polynomials piecewise cubics piecewise cubic polynomials parametric fitting nearest neighbourhoods natural cubic splines natural cubic spline multiple regression multi-predictor smoothers moving average fitted smooth fine grid evaluated-splines cubic-spline basis functions building block boundary knots bin smoother Euclidean distance Smoothing What is a smoother? Scatterplot smoothing: definition Parametric Regression Bin smoothers Running-mean and running-lines smoothers Kernel smoothers Computational issues Running medians and enhancements Equivalent kernels Regression splines Computational aspects Cubic smoothing splines Computational aspects Locally weighted running-line smoothers Smoothers for multiple predictors