PredictiveRegression (version 0.1-4)

gausspred: Gauss predictor

Description

Prediction intervals based on the Gauss linear model

Usage

gausspred(train,test,epsilons=c(0.05,0.01))

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%).

Value

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="" $b$="" $infinity$;="" 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.

References

Vovk, V., Nouretdinov, I., and Gammerman, A. (2009) On-line predictive linear regression. Annals of Statistics 37, 1566 - 1590. This paper describes this standard textbook procedure and its properties when used in the on-line mode.

Examples

  train <- matrix(c(1,2,3,4, 2.01,2.99,4.01,4.99), nrow=4, ncol=2);
  test <- matrix(c(0,10,20), nrow=3, ncol=1);
  output <- gausspred(train,test,c(0.05,0.2));
  print(output[[1]]);
  print(output[[2]]);