2004 for additive model method and basics of gamm; 2008 for generalized additive model method; 2006 for overview; 2003 for thin plate regression splines; 2000 is the original method, but no longer the default.

Wood, S.N. (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models.Journal of the American Statistical Association. 99:673-686.
Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society (B) 70(3):495-518
Wood, S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC.
Wood, S.N. (2003) Thin-plate regression splines. Journal of the Royal Statistical Society (B) 65(1):95-114.
Wood, S.N. (2000) Modelling and smoothing parameter estimation with multiple quadratic penalties. Journal of the Royal Statistical Society (B) 62(2):413-428.

Corresponding BibTeX entries:

  @Article{,
    title = {Stable and efficient multiple smoothing parameter
      estimation for generalized additive models},
    journal = {Journal of the American Statistical Association},
    volume = {99},
    number = {467},
    pages = {673-686},
    year = {2004},
    author = {S. N. Wood},
  }
  @Article{,
    title = {Fast stable direct fitting and smoothness selection for
      generalized additive models},
    journal = {Journal of the Royal Statistical Society (B)},
    volume = {70},
    number = {3},
    pages = {495-518},
    year = {2008},
    author = {S. N. Wood},
  }
  @Book{,
    title = {Generalized Additive Models: An Introduction with R},
    year = {2006},
    author = {S.N Wood},
    publisher = {Chapman and Hall/CRC},
  }
  @Article{,
    title = {Thin-plate regression splines},
    journal = {Journal of the Royal Statistical Society (B)},
    volume = {65},
    number = {1},
    pages = {95-114},
    year = {2003},
    author = {S. N. Wood},
  }
  @Article{,
    title = {Modelling and smoothing parameter estimation with multiple
      quadratic penalties},
    journal = {Journal of the Royal Statistical Society (B)},
    volume = {62},
    number = {2},
    pages = {413-428},
    year = {2000},
    author = {S. N. Wood},
  }