# curvefit: Test Equality of Curves with Homoscedastic or Heteroscedastic... In curvetest: The package will formally test two curves represented by discrete data sets to be statistically equal or not when the errors of the two curves were assumed either equal or not using the tube formula to calculate the tail probabilities.

## Description

Fit the smoothing curves.

## Usage

 ```1 2 3 4 5 6 7``` ```curvefit(formula, data, kernel = "Quartic", alpha = 0.5, bw = NULL, myx, bcorrect = "simple", getit = F) ## S3 method for class 'curvefit' print(x,...) ## S3 method for class 'curvefit' plot(x,y=NULL, add = F, get.data = TRUE, ...) ## S3 method for class 'curvefit' lines(x,...) ```

## Arguments

 `formula` A formula to the data set such as y~x. `data` A data frame of 2 columns representing the underlying curve. The column names must agree with the names in formula. `alpha` Smoothing parameter. Default=0.5. `bw` Window bandwidth for fitting the curve. `kernel` One of the kernel functions to use to fit the curves. Must be one of "Triangle", "Gaussian", "Trio","Uniform", "Triweight", "Epanechnikov", "Quartic". partial match is allowed. `myx` x-values in the test domain to calculate the curve values. `bcorrect` Boundary correction method. Right now, except for 'none', meaning no corrections, the only other opton is 'simple'. `getit` unused for this function. `add` logical, Tf true, add the curves to the plot.Otherwise, add fitted lines to the plot. `get.data` logical, not used in this function. `x` The fitted results from fitting the first or second curve by curvefit procedure. `y` dummy variable for compatible with parameters in the base definition of plot. `...` parameters for plot such as pch, lty, col etc.

## Details

For a 2 column data, the curve will be fitted according to formula using local regression method. Boundary corrections can be made. The fitted result will be returned as a 'curvefit' object, that can be plotted and printted by the associated S3 method print and plot.

## Value

An R object of class 'curvefit' will be generated including the fitted values of the curves with original specification of parameters.

## Author(s)

Zhongfa Zhang, Jiayang Sun

## References

Zhongfa Zhang, et al: Test Equality of Curves with Homoscedastic or Heteroscedastic Errors. To appear

 ```1 2 3 4 5 6 7 8``` ``` x=seq(0,1, length=n<-150); f<-function(x){x*(1-x)+sin(2*pi*x)}; y=f(x)+rnorm(n, 0, 0.5) fit<-curvefit(y~x,data.frame(x=x,y=y), bw=0.4,getit=T) plot(fit) lines(fit) fit ##print ```