The gss Package - NexTag Supports Open Source Initiatives

More documents

Recommendations

Info

40 ssden ssden Estimating Probability Density Using Smoothing Splines Description Usage Estimate probability densities using smoothing spline ANOVA models. The symbolic model specification via formula follows the same rules as in lm, but with the response missing. ssden(formula, type=NULL, data=list(), alpha=1.4, weights=NULL, subset, na.action=na.omit, id.basis=NULL, nbasis=NULL, seed=NULL, domain=as.list(NULL), quadrature=NULL, prec=1e-7, maxiter=30) Arguments formula type data alpha weights subset na.action id.basis nbasis seed domain quadrature prec maxiter Symbolic description of the model to be fit. List specifying the type of spline for each variable. See mkterm for details. Optional data frame containing the variables in the model. Parameter defining cross-validation score for smoothing parameter selection. Optional vector of bin-counts for histogram data. Optional vector specifying a subset of observations to be used in the fitting process. Function which indicates what should happen when the data contain NAs. Index of observations to be used as "knots." Number of "knots" to be used. Ignored when id.basis is specified. Seed to be used for the random generation of "knots." Ignored when id.basis is specified. Data frame specifying marginal support of density. Quadrature for calculating integral. Mandatory if variables other than factors or numerical vectors are involved. Precision requirement for internal iterations. Maximum number of iterations allowed for internal iterations. Details The model specification via formula is for the log density. For example, ~x1*x2 prescribes a model of the form logf(x1, x2) = g 1 (x1) + g 2 (x2) + g 12 (x1, x2) + C with the terms denoted by "x1", "x2", and "x1:x2"; the constant is determined by the fact that a density integrates to one.
ssden 41 The selective term elimination may characterize (conditional) independence structures between variables. For example, ~x1*x2+x1*x3 yields the conditional independence of x2 and x3 given x1. Parallel to those in a ssanova object, the model terms are sums of unpenalized and penalized terms. Attached to every penalized term there is a smoothing parameter, and the model complexity is largely determined by the number of smoothing parameters. The selection of smoothing parameters is through a cross-validation mechanism described in the references, with a parameter alpha; alpha=1 is "unbiased" for the minimization of Kullback- Leibler loss but may yield severe undersmoothing, whereas larger alpha yields smoother estimates. A subset of the observations are selected as "knots." Unless specified via id.basis or nbasis, the number of "knots" q is determined by max(30, 10n 2/9 ), which is appropriate for the default cubic splines for numerical vectors. Value ssden returns a list object of class "ssden". dssden and cdssden can be used to evaluate the estimated joint density and conditional density; pssden, qssden, cpssden, and cqssden can be used to evaluate (conditional) cdf and quantiles. The method project.ssden can be used to calculate the Kullback-Leibler projection for model selection. Note Default quadrature will be constructed for up to 4 numerical vectors on a hyper cube, then outer product with factor levels will be taken if factors are involved. The sides of the hyper cube are specified by domain; for domain$x missing, the default is c(min(x),max(x))+c(- 1,1)*(max(x)-mimn(x))*.05. On a 1-D interval, the quadrature is the 200-point Gauss-Legendre formula returned from gauss.quad. For 2, 3, or 4 numerical vectors, delayed Smolyak cubatures from smolyak.quad with 449, 2527, and 13697 points are used on cubes with the marginals properly transformed; see Gu and Wang (2003) for the marginal transformations. The results may vary from run to run. For consistency, specify id.basis or set seed. Author(s) Chong Gu, 〈chong@stat.purdue.edu〉 References Gu, C. (2002), Smoothing Spline ANOVA Models. New York: Springer-Verlag. Gu, C. and Wang, J. (2003), Penalized likelihood density estimation: Direct cross-validation and scalable approximation. Statistica Sinica, 13, 811–826.
Page 1 and 2: The gss Package February 16, 2008 V
Page 3 and 4: aids 3 Source Douglas, A. and Delam
Page 5 and 6: cdssden 5 Format Source A vector of
Page 7 and 8: dssden 7 References Gu, C. (2002),
Page 9 and 10: family 9 cfit.nbinomial(y, wt, offs
Page 11 and 12: gauss.quad 11 Source Moreau, T., O
Page 13 and 14: gssanova 13 Value gssanova returns
Page 15 and 16: gssanova0 15 data weights subset Op
Page 17 and 18: hzdrate.sshzd 17 ## Not run: rm(tes
Page 19 and 20: mkfun.tp 19 See Also mkterm, mkfun.
Page 21 and 22: mkran 21 The Z matrix is determined
Page 23 and 24: mkterm 23 mkterm Assembling Model T
Page 25 and 26: nlm0 25 fit1
Page 27 and 28: ozone 27 Format A data frame contai
Page 29 and 30: predict.ssanova 29 Value For se.fit
Page 31 and 32: project 31 project Projecting Smoot
Page 33 and 34: kpk0 33 nu varht random dc sr y0 Op
Page 35 and 36: ssanova 35 Arguments d k Dimension
Page 37 and 38: ssanova0 37 References Gu, C. (2002
Page 39: ssanova0 39 Note For complex models
Page 43 and 44: sshzd 43 Description Estimate hazar
Page 45 and 46: summary.gssanova 45 ## Not run: dat
Page 47 and 48: summary.gssanova0 47 References Gu,
Page 49 and 50: wesdr 49 Value summary.ssanova retu
Page 51 and 52: Index ∗Topic datasets aids, 2 bac
Page 53: INDEX 53 mkrk.sphere, 22 mkrk.spher

The gss Package - NexTag Supports Open Source Initiatives

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?