Data given in pairs, (t1i,…tpi,z1i,…,zqi,yi), i = 1,2,…,n which follows the nonparametric regression model multivariable predictors of additives: (Formula presented) The regression curve gr(tr), r =1,2,…,p and hs(zs), s = 1,2,…,q assumed smooth, and each approached using Spline function truncated and Kernel functions. Nonparametric regression curve estimation multivariable predictor truncated Spline and Kernel mixed obtained from optimization: (Formula presented) Truncated Spline component multivariable estimator, multivariable Kernel component, and a mixture of truncated Spline and Kernel are follow: (Formula presented) Truncated Spline components multivariable estimator, Kernel multivariable components, and mix Spline Kernel truncated and each is a biased estimator, but it is a linear estimator class under observation. Spline Estimator mixture truncated and multivariable Kernel is depend on the points of knot K and bandwidth parameters. The mix of Truncted Spline and multivariable Kernel Estimator associated with knot K optimal and optimal bandwidth parameters. Point knot and optimal bandwidth parameters derived from minimum of Generalized Cross Validation (GCV).

Original languageEnglish
Pages (from-to)5047-5057
Number of pages11
JournalGlobal Journal of Pure and Applied Mathematics
Issue number6
Publication statusPublished - 2016


  • Mixed Estimator
  • Multivariable Kernel
  • MultivariableTruncated Spline
  • Nonparametric Regression


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