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.

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 2.2-5.6 Index]