# Bootstrap Kolmogorov-Smirnov

### Description

This function executes a bootstrap version of the univariate Kolmogorov-Smirnov test which provides correct coverage even when the distributions being compared are not entirely continuous. Ties are allowed with this test unlike the traditional Kolmogorov-Smirnov test.

### Usage

1 2 |

### Arguments

`Tr` |
A vector containing the treatment observations. |

`Co` |
A vector containing the control observations. |

`nboots` |
The number of bootstraps to be performed. These are, in fact, really Monte Carlo simulations which are preformed in order to determine the proper p-value from the empiric. |

`alternative` |
indicates the alternative hypothesis and must be one of
'"two.sided"' (default), '"less"', or '"greater"'. You can
specify just the initial letter. See |

`print.level` |
If this is greater than 1, then the simulation count is printed out while the simulations are being done. |

### Value

`ks.boot.pvalue` |
The bootstrap p-value of the Kolmogorov-Smirnov test for the hypothesis that the probability densities for both the treated and control groups are the same. |

`ks` |
Return object from |

`nboots` |
The number of bootstraps which were completed. |

### Author(s)

Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, http://sekhon.berkeley.edu/.

### References

Sekhon, Jasjeet S. 2011. "Multivariate and Propensity Score
Matching Software with Automated Balance Optimization.”
*Journal of Statistical Software* 42(7): 1-52.
http://www.jstatsoft.org/v42/i07/

Diamond, Alexis and Jasjeet S. Sekhon. 2013. "Genetic Matching for
Estimating Causal Effects: A General Multivariate Matching Method for
Achieving Balance in Observational Studies.” *Review of
Economics and Statistics*. 95 (3): 932–945.
http://sekhon.berkeley.edu/papers/GenMatch.pdf

Abadie, Alberto. 2002. “Bootstrap Tests for Distributional Treatment
Effects in Instrumental Variable Models.” *Journal of the
American Statistical Association*, 97:457 (March) 284-292.

### See Also

Also see `summary.ks.boot`

,
`qqstats`

, `balanceUV`

, `Match`

,
`GenMatch`

, `MatchBalance`

,
`GerberGreenImai`

, `lalonde`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | ```
#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
#
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)
#
# Do we have balance on 1975 income after matching?
#
ks <- ks.boot(lalonde$re75[rr$index.treated], lalonde$re75[rr$index.control], nboots=500)
summary(ks)
``` |