`crssigtest`

implements a consistent test of significance of
an explanatory variable in a nonparametric regression setting that is
analogous to a simple \(t\)-test in a parametric regression
setting. The test is based on Ma and Racine (2011).

```
crssigtest(model = NULL,
index = NULL,
boot.num = 399,
boot.type = c("residual","reorder"),
random.seed = 42,
boot = TRUE)
```

model

a `crs`

model object.

index

a vector of indices for the columns of `model$xz`

for which the
test of significance is to be conducted. Defaults to (1,2,…,\(p\))
where \(p\) is the number of columns in `model$xz`

.

boot.num

an integer value specifying the number of bootstrap replications to
use. Defaults to `399`

.

boot.type

whether to conduct ‘residual’ bootstrapping (iid) or permute (reorder) in place the predictor being tested when imposing the null.

random.seed

an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.

boot

a logical value (default `TRUE`

) indicating whether to compute
the bootstrap P-value or simply return the asymptotic P-value.

`crssigtest`

returns an object of type
`sigtest`

. `summary`

supports `sigtest`

objects. It has the following components:

the vector of indices input

the vector of bootstrap P-values for each statistic in `F`

the vector of asymptotic P-values for each statistic in index

the vector of pseudo F-statistics `F`

the matrix of bootstrapped pseudo F-statistics
generated under the null (one column for each statistic in `F`

)

the vector of numerator degrees of freedom for each
statistic in `F`

(based on the smoother matrix)

the vector of denominator degrees of freedom for each
statistic in `F`

(based on the smoother matrix)

the vector of restricted sums of squared residuals for
each statistic in `F`

the vector of unrestricted sums of squared residuals for
each statistic in `F`

the number of bootstrap replications

the `boot.type`

the names of the variables in `model$xz`

This function should be considered to be in ‘beta status’ until further notice.

Caution: bootstrap methods are, by their nature, *computationally
intensive*. This can be frustrating for users possessing large
datasets. For exploratory purposes, you may wish to override the
default number of bootstrap replications, say, setting them to
`boot.num=99`

.

Li, Q. and J.S. Racine (2007), *Nonparametric Econometrics:
Theory and Practice,* Princeton University Press.

Ma, S. and J.S. Racine, (2011), “Inference for Regression Splines with Categorical and Continuous Predictors,” Working Paper.

# NOT RUN { options(crs.messages=FALSE) set.seed(42) n <- 1000 z <- rbinom(n,1,.5) x1 <- rnorm(n) x2 <- runif(n,-2,2) z <- factor(z) ## z is irrelevant y <- x1 + x2 + rnorm(n) model <- crs(y~x1+x2+z,complexity="degree",segments=c(1,1)) summary(model) model.sigtest <- crssigtest(model) summary(model.sigtest) # }