# lpme: Local Polynomial Estimators for the Errors-in-Variables...

Description Usage Arguments Details Value Author(s) References Examples

### Description

This function provides both the DFC (Delaigle, Fan, and Carroll, 2009) and HZ (Huang and Zhou, 2014+) local polynomial estimators for solving the errors-in-variables problem.

### Usage

 ```1 2``` ```lpme(Y, W, bw, method="HZ", sig=NULL, error="laplace", xgridmin=-2, xgridmax=2, data=sys.frame(sys.parent()), na.action=na.fail, work.dir=NULL) ```

### Arguments

 `Y` an n by 1 response vector. `W` an n by 1 predictor vector. `bw` bandwidth. `method` the method to be used; `method="HZ"` returns the estimator proposed by Huang and Zhou (2015); `method="DFC"` returns the estimator proposed by Delaigle, Fan, and Carroll (2009); `method="naive"` returns the local polynomial estimator ignoring measurement error. `sig` standard deviation of the measurement error. `error` the distribution assumed for the measurement error; `error="laplace"` is for Laplace distribution; `error="normal"` is for Gaussian distribution. `xgridmin` the minimum value where the estimated responsed is evaluated at; default is -2. `xgridmax` the maximum value where the estimated responsed is evaluated at; defualt is 2. `data` data frame. `na.action` a function that indicates what should happen when the data contain `NA`s. The default action (`na.fail`) causes `lpme` to print an error message and terminate if there are any incomplete observations. `work.dir` working directory.

### Details

This function provides both the DFC (Delaigle, Fan, and Carroll, 2009) and HZ (Huang and Zhou, 2014+) local polynomial estimators for solving the errors-in-variables problem.

### Value

The results include the grid points for predictor `xgrid` and corresponding fitted responses `yhat`.

### Author(s)

Haiming Zhou <zhouh@email.sc.edu> and Xianzheng Huang <huang@stat.sc.edu>

### References

Delaigle, A. and Hall, P. (2008). Using SIMEX for smoothing-parameter choice in errors-in-variables problems. Journal of the American Statistical Association, 103, 280-287.

Delaigle, A., Fan, J., and Carroll, R. (2009). A design-adaptive local polynomial estimator for the errors-in-variables problem. Journal of the American Statistical Association 104, 348-359.

Huang, X. and Zhou, H. (2014+). An alternative local polynomial estimator for the errors-in-variable problem. Submitted.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```############################################# ## X - True covariates ## W - Observed covariates ## Y - individual response rm(list=ls()) library(lpme) ## sample size: n =100; ## Function gofx(x) to estimate gofx = function(x){ 1/4*x + x^2/4 } ## Generate data sigma_e = 0.5; sigma_x = 1; X = rnorm(n, 0, sigma_x); ## Sample Y Y = gofx(X) + rnorm(n, 0, sigma_e); ##------------------ method Based on X --------------------------- #ghat_X= lpme(Y, X, 0.1, method="naive"); ## reliability ratio lambda=0.85; sigma_u = sqrt(1/lambda-1)*sigma_x; print( sigma_x^2/(sigma_x^2 + sigma_u^2) ); W=X+rnorm(n,0,sigma_u); #W=X+rlaplace(n,0,sigma_u/sqrt(2)); ##------------------ method Based on W --------------------------- #ghat_W=lpme(Y, W, 0.1, method="naive"); ##------------------ JASA method ------------------------------------- h = 0.13; #ghat_JASA = lpme(Y, W, h, method="DFC", sig=sigma_u, error="laplace"); ##------------------ Our method ------------------------- ghat_NEW = lpme(Y, W, h, method="HZ", sig=sigma_u, error="laplace"); ## plots x = ghat_NEW\$xgrid; plot(x, gofx(x), "l", main="Individual", lwd="2") lines(ghat_NEW\$xgrid, ghat_NEW\$yhat, lty="dashed", col="2",lwd="3") #lines(ghat_JASA\$xgrid, ghat_JASA\$yhat, lty="dotted", col="3",lwd="3") #lines(ghat_X\$xgrid, ghat_X\$yhat, lty="dashed", col="4",lwd="2") #lines(ghat_W\$xgrid, ghat_W\$yhat, lty="dashed", col="5",lwd="3") ```

Search within the lpme package
Search all R packages, documentation and source code

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.