predict_dim {CVarE} R Documentation

## Estimate Dimension of the Sufficient Reduction.

### Description

This function estimates the dimension, i.e. the rank of B. The default method `'CV'` performs leave-one-out (LOO) cross-validation using `mars` as follows for `k = min.dim, ..., max.dim` a cross-validation via `mars` is performed on the dataset (Y_i, B_k' X_i)_{i = 1, ..., n} where B_k is the p x k dimensional CVE estimate. The estimated SDR dimension is the k where the cross-validation mean squared error is minimal. The method `'elbow'` estimates the dimension via k = argmin_k L_n(V_{p - k}) where V_{p - k} is the space that is orthogonal to the column space of the CVE estimate of B_k. Method `'wilcoxon'` finds the minimum using the Wilcoxon test.

### Usage

```predict_dim(object, ..., method = "CV")
```

### Arguments

 `object` an object of class `"cve"`, usually, a result of a call to `cve` or `cve.call`. `...` ignored. `method` This parameter specifies which method is used in dimension estimation. It provides three options: `'CV'` (default), `'elbow'` and `'wilcoxon'`.

### Value

A `list` with

criterion for method and `k = min.dim, ..., max.dim`.

k

estimated dimension is the minimizer of the criterion.

### Examples

```# create B for simulation
B <- rep(1, 5) / sqrt(5)

set.seed(21)
# creat predictor data x ~ N(0, I_p)
x <- matrix(rnorm(500), 100)

# simulate response variable
#    y = f(B'x) + err
# with f(x1) = x1 and err ~ N(0, 0.25^2)
y <- x %*% B + 0.25 * rnorm(100)

# Calculate cve for unknown k between min.dim and max.dim.
cve.obj.simple <- cve(y ~ x)

predict_dim(cve.obj.simple)

```

[Package CVarE version 1.1 Index]