To perform nonparametric regression with errors-in-variables. The measurement errors can be either homoscedastic or heteroscedastic.

1 2 |

`y` |
The observed data. It is a vector of length at least 3. |

`sig` |
The standard deviations |

`z` |
z is the dependent variable. |

`x` |
x is user-defined grids where the regression function will be evaluated. FFT method is not applicable if x is given. |

`error` |
Error distribution types: (1) 'normal' for normal errors; (2) 'laplacian' for Laplacian errors; (3) 'snormal' for a special case of small normal errors. |

`bw` |
Specifies the bandwidth. It can be a single numeric value which has been pre-determined; or computed with the specific bandwidth selector: 'dnrd' to compute the rule-of-thumb plugin bandwidth as suggested by Fan (1991); 'dmise' to compute the plugin bandwidth by minimizing MISE; 'dboot1' to compute the bootstrap bandwidth selector without resampling (Delaigle and Gijbels, 2004a), which minimizing the MISE bootstrap bandwidth selectors; 'boot2' to compute the smoothed bootstrap bandwidth selector with resampling. |

`adjust` |
adjust the range there the regression function is to be evaluated. By default, |

`n` |
number of points where the regression function is to be evaluated. |

`from` |
the starting point where the regression functionF is to be evaluated. |

`to` |
the starting point where the regression function is to be evaluated. |

`cut` |
used to adjust the starting end ending points where the regression function is to be evaluated. |

`na.rm` |
is set to FALSE by default: no NA value is allowed. |

`grid` |
the grid number to search the optimal bandwidth when a bandwidth selector was specified in bw. Default value "grid=100". |

`ub` |
the upper boundary to search the optimal bandwidth, default value is "ub=2". |

`...` |
control |

FFT is currently not supported for nonparametric regression.

An object of class “Decon”.

X.F. Wang wangx6@ccf.org

B. Wang bwang@jaguar1.usouthal.edu

Fan, J. and Truong, Y.K. (1993). Nonparametric regression with errors in variables. *Annals of
Statistics*, 21(4), 1900-1925.

Delaigle, A. and Meister, A. (2007). Nonparametric regression estimation in the heteroscedastic errors-in-variables problem. *Journal of the American Statistical Association*, 102, 1416-1426.

Wang, X.F. and Wang, B. (2011). Deconvolution estimation in measurement error models: The R package decon. *Journal of Statistical Software*, 39(10), 1-24.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
n <- 2000
x <- c(rnorm(n/2,2,1), rnorm(n/2, -2,1))
sig <- .8
u <- sig*rnorm(n)
w <- x+u
e <- rnorm(n, sd=0.2)
y <- x^2-2*x+e
bw1 <- bw.dboot1(w, sig)
# estimate the unknown density with measurement error
(m1 <- DeconNpr(w, sig, y ,error="normal", from=0.9*min(x), to=0.9*max(x)))
# plot the results
plot(m1, col="red", lwd=3, lty=2, xlab="x", ylab="m(x)", main="",
zero.line=FALSE)
lines(ksmooth(x,y, kernel = "normal", 2, range.x=c(0.9*min(x),0.9*max(x))),
lwd=3, lty=1)
lines(ksmooth(w,y, kernel = "normal", 2, range.x=c(0.9*min(x),0.9*max(x))),
col="blue", lwd=3, lty=3)
``` |

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