# Compute the K statistics of Kleibergen

### Description

The test is proposed by Kleibergen (2005). It is robust to weak identification.

### Usage

1 2 3 |

### Arguments

`obj` |
Object of class "gmm" returned by |

`theta0` |
The null hypothesis being tested. See details. |

`alphaK, alphaJ` |
The size of the J and K tests when combining the two. The overall size is alphaK+alphaJ. |

`x` |
An object of class |

`digits` |
The number of digits to be printed |

`...` |
Other arguments when |

### Details

The function produces the J-test and K-statistics which are robust to weak identification. The test is either *H0:θ=theta_0*, in which case theta0 must be provided, or *β=β_0*, where *θ=(α', β')'*, and *α* is assumed to be identified. In the latter case, theta0 is NULL and obj is a restricted estimation in which *β* is fixed to *β_0*. See `gmm`

and the option "eqConst" for more details.

### Value

Tests and p-values

### References

Keibergen, F. (2005),
Testing Parameters in GMM without assuming that they are identified.
*Econometrica*, **73**,
1103-1123,

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
library(mvtnorm)
sig <- matrix(c(1,.5,.5,1),2,2)
n <- 400
e <- rmvnorm(n,sigma=sig)
x4 <- rnorm(n)
w <- exp(-x4^2) + e[,1]
y <- 0.1*w + e[,2]
h <- cbind(x4, x4^2, x4^3, x4^6)
g3 <- y~w
res <- gmm(g3,h)
# Testing the whole vector:
KTest(res,theta0=c(0,.1))
# Testing a subset of the vector (See \code{\link{gmm}})
res2 <- gmm(g3, h, eqConst=matrix(c(2,.1),1,2))
res2
KTest(res2)
``` |