iidpred: IID predictor

In PredictiveRegression: Prediction Intervals for Three Basic Statistical Models

Description

Prediction intervals based on the IID model

Usage

iidpred(train,test,epsilons=c(0.05,0.01),ridge=0)

Arguments

train	Training set as a matrix of size N times K+1. Each row describes an observation. Columns 1 to K are the explanatory variables, and column K+1 is the response variables.
test	Test set as a matrix of size N2 times K. Each row corresponds to an observation (but without the response variable). Columns 1 to K are the explanatory variables.
epsilons	Vector of several significance levels. Each significance level epsilons[j] is a number between 0 and 1. The default value is (5%,1%).
ridge	Ridge coefficient, a nonnegative number. The default value is 0; setting it to a small positive constant might lead to more stable results.

Value

The output is a list of three elements.

output[[1]]	The matrix of lower bounds of prediction intervals. Its size is N2 times Neps, where N2 is the number of test observations and Neps is the number of significance levels. The element output[[1]][i,j] of output[[1]] is the lower bound a of the prediction interval [a,b] for the i-th test observation and for the j-th significance level epsilons[j] in the vector epsilons.
output[[2]]	The matrix of upper bounds b, with the same structure as output[[1]]. Typically a =output[[1]][i,j] and b = output[[2]][i,j] are real numbers such that a <= b. Exceptions: a is allowed to be -infinity and b is allowed to be infinity; the only case where a > b is a = infinity and b = -infinity (the empty prediction [a,b]).
output[[3]]	The termination code: 0 = normal termination; 1 = illegal parameters (the training and test sets have different numbers of explanatory variables); 2 = too few observations for all significance levels.

References

Vovk, V., Nouretdinov, I., and Gammerman, A. (2009) On-line predictive linear regression. Annals of Statistics 37, 1566 - 1590. The new arXiv version http://arxiv.org/abs/math/0511522 of this paper contains the description of this program and the algorithm that this program implements.

Vovk, V., Gammerman, A., and Shafer, G. (2005) Algorithmic Learning in a Random World. New York: Springer. This program implements the algorithm described on pages 30 - 34 of this book.

Examples

  train <- matrix(c(0,10,20,30, 1.01,10.99,21.01,30.99), nrow=4, ncol=2);
  test <- matrix(c(5,15,25), nrow=3, ncol=1);
  output <- iidpred(train,test,c(0.05,0.2),0.01);
  print(output[[1]]);
  print(output[[2]]);

PredictiveRegression documentation built on May 2, 2019, 8:16 a.m.