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