### Abstract

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positivedefinite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n =50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

Original language | English |
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Pages (from-to) | 491-556 |

Number of pages | 66 |

Journal | Advances in Econometrics |

Volume | 33 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Cite this

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*Advances in Econometrics*, vol. 33, pp. 491-556. https://doi.org/10.1108/S0731-905320140000033014

**Testing the equality of two positive-definite matrices with application to informationmatrix testing.** / Cho, Jin Seo; White, Halbert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Testing the equality of two positive-definite matrices with application to informationmatrix testing

AU - Cho, Jin Seo

AU - White, Halbert

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positivedefinite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n =50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

AB - We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positivedefinite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n =50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

UR - http://www.scopus.com/inward/record.url?scp=84912565684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84912565684&partnerID=8YFLogxK

U2 - 10.1108/S0731-905320140000033014

DO - 10.1108/S0731-905320140000033014

M3 - Article

AN - SCOPUS:84912565684

VL - 33

SP - 491

EP - 556

JO - Advances in Econometrics

JF - Advances in Econometrics

SN - 0731-9053

ER -