R: Estimation of the error standard deviation in nonparametric...

sm.sigma {sm} | R Documentation

## Estimation of the error standard deviation in nonparametric regression.

### Description

This function estimates the error standard deviation in nonparametric regression with one or two covariates.

### Usage

    sm.sigma(x, y, rawdata = NA, weights = rep(1, length(y)),
                   diff.ord = 2, ci = FALSE, model = "none", h = NA, ...)

### Arguments

`x` | a vector or two-column matrix of covariate values.
`y` | a vector of responses.
`rawdata` | a list containing the output from a binning operation. This argument is used by `sm.regression` and it need not be set for direct calls of the function.
`weights` | a list of frequencies associated with binned data. This argument is used by `sm.regression` and it need not be set for direct calls of the function.
`diff.ord` | an integer value which determines first (1) or second (2) differencing in the estimation of sigma.
`ci` | a logical value which controls whether a confidence interval is produced.
`model` | a character variable. If this is set to `"constant"` then a test of constant variance over the covariates is performed (only in the case of two covariates)
`h` | a vector of length two defining a smoothing parameter to be used in the test of constant variance.
`...` | other optional parameters are passed to the `sm.options` function, through a mechanism which limits their effect only to this call of the function; the only one relevant for this function is `nbins`.

### Details

see the reference below.

### Value

a list containing the estimate and, in the two covariate case, a matrix which can be used by the function `sm.sigma2.compare`, pseudo-residuals and, if appropriate, a confidence interval and a p-value for the test of constant variance.

### Side Effects

none.

### References

Bock, M., Bowman, A.W.\ \& Ismail, B. (2007). Estimation and inference for error variance in bivariate nonparametric regression. Statistics \& Computing, to appear.

### See Also

`sm.sigma2.compare`

### Examples

    ## Not run:
    with(airquality, {
       x     <- cbind(Wind, Temp)
       y     <- Ozone^(1/3)
       group <- (Solar.R < 200)
       sig1 <- sm.sigma(x[ group, ], y[ group], ci = TRUE)
       sig2 <- sm.sigma(x[!group, ], y[!group], ci = TRUE)
       print(c(sig1$estimate, sig1$ci))
       print(c(sig2$estimate, sig2$ci))
       print(sm.sigma(x[ group, ], y[ group], model = "constant", h = c(3, 5))$p)
       print(sm.sigma(x[!group, ], y[!group], model = "constant", h = c(3, 5))$p)
       print(sm.sigma2.compare(x[group, ], y[group], x[!group, ], y[!group]))
    })

    ## End(Not run)

[Package sm version 2.2-5.4 Index]