# predict_Ohit: Make predictions based on a fitted "Ohit" object In Ohit: OGA+HDIC+Trim and High-Dimensional Linear Regression Models

## Description

This function returns predictions from a fitted "Ohit" object.

## Usage

 1 predict_Ohit(object, newX)

## Arguments

 object Fitted "Ohit" model object. newX Matrix of new values for X at which predictions are to be made.

## Value

 pred_HDIC The predicted value based on the model determined by OGA+HDIC. pred_Trim The predicted value based on the model determined by OGA+HDIC+Trim.

## Author(s)

Hai-Tang Chiou, Ching-Kang Ing and Tze Leung Lai.

## References

Ing, C.-K. and Lai, T. L. (2011). A stepwise regression method and consistent model selection for high-dimensional sparse linear models. Statistica Sinica, 21, 1473–1513.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # Example setup (Example 3 in Section 5 of Ing and Lai (2011)) n = 410 p = 4000 q = 10 beta_1q = c(3, 3.75, 4.5, 5.25, 6, 6.75, 7.5, 8.25, 9, 9.75) b = sqrt(3/(4 * q)) x_relevant = matrix(rnorm(n * q), n, q) d = matrix(rnorm(n * (p - q), 0, 0.5), n, p - q) x_relevant_sum = apply(x_relevant, 1, sum) x_irrelevant = apply(d, 2, function(a) a + b * x_relevant_sum) X = cbind(x_relevant, x_irrelevant) epsilon = rnorm(n) y = as.vector((x_relevant %*% beta_1q) + epsilon) # with intercept fit1 = Ohit(X[1:400, ], y[1:400]) predict_Ohit(fit1, rbind(X[401:401, ])) predict_Ohit(fit1, X[401:410, ]) # without intercept fit2 = Ohit(X[1:400, ], y[1:400], intercept = FALSE) predict_Ohit(fit2, rbind(X[401:401, ])) predict_Ohit(fit2, X[401:410, ])

### Example output

\$pred_HDIC
[1] 16.18587

\$pred_Trim
[1] 16.16235

\$pred_HDIC
[1]  16.1858664  -3.2580596 -21.3708495 -17.3621501  -9.2934443  -1.6120540
[7]  18.5471672 -11.6529395 -33.3141578   0.6153522

\$pred_Trim
[1]  16.1623475  -3.2242840 -21.4416871 -17.4033878  -9.2498644  -1.6231749
[7]  18.5459885 -11.5762733 -33.2060854   0.5952212

\$pred_HDIC
[1] 16.18521

\$pred_Trim
[1] 16.16174

\$pred_HDIC
[1]  16.1852111  -3.2588039 -21.3717391 -17.3630388  -9.2941446  -1.6126408
[7]  18.5461139 -11.6535413 -33.3148442   0.6146596

\$pred_Trim
[1]  16.1617442  -3.2249725 -21.4424906 -17.4041887  -9.2504693  -1.6236990
[7]  18.5450519 -11.5768345 -33.2066904   0.5945924

Ohit documentation built on May 1, 2019, 8:43 p.m.