## The Annals of Statistics

- Ann. Statist.
- Volume 14, Number 1 (1986), 250-264.

### Rank Tests for Independence for Bivariate Censored Data

#### Abstract

The paper discusses statistics that can be used to test whether two failure times, say $X_1$ and $X_2$, are independent. The two variables are subject to right censoring so that what is observed is $Y_i = \min(X_i, Z_i)$ and $\delta_i = I(X_i = Y_i)$, where $(Z_1, Z_2)$ are censoring times independent of $(X_1, X_2)$. Statistics that generalize the Spearman rank correlation and the log-rank correlation are considered, as well as general linear rank statistics. The Chernoff-Savage approach is adopted to show that suitably standardized versions of these statistics are asymptotically normal under both fixed and converging alternatives.

#### Article information

**Source**

Ann. Statist., Volume 14, Number 1 (1986), 250-264.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176349853

**Digital Object Identifier**

doi:10.1214/aos/1176349853

**Mathematical Reviews number (MathSciNet)**

MR829566

**Zentralblatt MATH identifier**

0597.62035

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62N05: Reliability and life testing [See also 90B25]

**Keywords**

Bivariate censoring rank correlation statistics

#### Citation

Dabrowska, Dorota M. Rank Tests for Independence for Bivariate Censored Data. Ann. Statist. 14 (1986), no. 1, 250--264. doi:10.1214/aos/1176349853. https://projecteuclid.org/euclid.aos/1176349853