Testing Quasi-independence for Truncation Data

Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that includes existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes

Testing Quasi-independence for Truncation Data

Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that includes existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes

What would Nelson and Plosser find had they used panel unit root tests?

In this study, we systemically apply nine recent panel unit root tests to the same fourteen macroeconomic and financial series as those considered in the seminal paper by Nelson and Plosser (1982). The data cover OECD countries from 1950 to 2003. Our results clearly point out the difficulty that applied econometricians would face when they want to get a simple and clear-cut diagnosis with panel unit root tests. We confirm the fact that panel methods must be very carefully used for testing unit roots in macroeconomic or financial panels. More precisely, we find mitigated results under the cross-sectional independence assumption, since the unit root hypothesis is rejected for many macroeconomic variables. When international cross-correlations are taken into account, conclusions depend on the specification of these cross-sectional dependencies. Two groups of tests can be distinguished. The first group tests are based on a dynamic factor structure or an error component model. In this case, the non stationarity of common factors (international business cycles or growth trends) is not rejected, but the results are less clear with respect to idiosyncratic components. The second group tests are based on more general specifications. Their results are globally more favourable to the unit root assumption.Panel Unit Root Tests

Testing the assumptions for the analysis of survival data arising from a prevalent cohort study with follow-up

In a prevalent cohort study with follow-up subjects identified as prevalent cases are followed until failure (defined suitably) or censoring. When the dates of the initiating events of these prevalent cases are ascertainable, each observed datum point consists of a backward recurrence time and a possibly censored forward recurrence time. Their sum is well known to be the left truncated lifetime. It is common to term these left truncated lifetimes "length biased" if the initiating event times of all the incident cases (including those not observed through the prevalent sampling scheme) follow a stationary Poisson process. Statistical inference is then said to be carried out under stationarity. Whether or not stationarity holds, a further assumption needed for estimation of the incident survivor function is the independence of the lifetimes and their accompanying truncation times. That is, it must be assumed that survival does not depend on the calendar date of the initiating event. We show how this assumption may be checked under stationarity, even though only the backward recurrence times and their associated (possibly censored) forward recurrence times are\ud observed. We prove that independence of the lifetimes and truncation times is equivalent to equality in distribution of the backward and forward recurrence times, and exploit this equivalence as a means of testing the former hypothesis. A simulation study is conducted to investigate the power and Type 1 error rate of our proposed tests, which include a bootstrap procedure that takes into account the pairwise dependence between the forward and backward recurrence times, as well as the potential censoring of only one of the members of each pair. We illustrate our methods using data from the Canadian Study of Health and Aging. We also point out an equivalence of the\ud problem presented here to a non-standard changepoint problem