Loess Bootstrap

Bootstrap of a Local Polynomial Regression (loess)

The function fits a loess curve and then calculates a symmetric nonparametric bootstrap with a confidence region. Fitted curves are evaluated at a fixed number of equally-spaced x values, regardless of the number of x values in the data. Some replicates do not include the values at the lower and upper end of the range of x values. If the number of such replicates is too large, it becomes impossible to construct a confidence region that includes a fraction "confidence" of the bootstrap replicates. In such cases, the left and/or right portion of the confidence region is truncated.

loess.boot(x, y, nreps = 100, confidence = 0.95, ...)

Arguments

x	Independent variable
y	Dependent variable
nreps	Number of bootstrap replicates
confidence	Fraction of replicates contained in confidence region
...	Additional arguments passed to loess function

Value

list object containing

• nreps Number of bootstrap replicates

• confidence Confidence interval (region)

• span alpha (span) parameter used loess fit

• degree polynomial degree used in loess fit

• normalize Normalized data (TRUE/FALSE)

• family Family of statistic used in fit

• parametric Parametric approximation (TRUE/FALSE)

• surface Surface fit, see loess.control

• data data.frame of x,y used in model

• fit data.frame including:

  1. x - Equally-spaced x index (see NOTES)

  2. y.fit - loess fit

  3. up.lim - Upper confidence interval

  4. low.lim - Lower confidence interval

  5. stddev - Standard deviation of loess fit at each x value

References

Cleveland, WS, (1979) Robust Locally Weighted Regression and Smoothing Plots Journal of the American Statistical Association 74:829-836

Efron, B., and R. Tibshirani (1993) An Introduction to the Bootstrap Chapman and Hall, New York

Hardle, W., (1989) Applied Nonparametric Regression Cambridge University Press, NY.

Tibshirani, R. (1988) Variance stabilization and the bootstrap. Biometrika 75(3):433-44.

Author

Jeffrey S. Evans jeffrey_evans@tnc.org

Examples

 n=1000
 x <- seq(0, 4, length.out=n)   
 y <- sin(2*x)+ 0.5*x + rnorm(n, sd=0.5)
 sb <- loess.boot(x, y, nreps=99, confidence=0.90, span=0.40)
 plot(sb)