Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order $1/n$. In the second, we give multivariate generalizations of the Lugannani--Rice and Barndorff-Nielsen or $r^*$ formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the $k$ sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.Comment: Published in at http://dx.doi.org/10.1214/11-AOS945 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Relative errors for bootstrap approximations of the serial correlation coefficient

We consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is necessary to consider bootstrap approximations for tests based on the statistic since the distribution of errors is unknown. We obtain saddle-point approximations for tail probabilities of the statistic and its bootstrap version and use these to show that the bootstrap tail probabilities approximate the true values with given relative errors, thus extending the classical results of Daniels [Biometrika 43 (1956) 169-185] for the Gaussian case. The methods require conditioning on the set of odd numbered observations and suggest a conditional bootstrap which we show has similar relative error properties.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1111 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

RISK MANAGEMENT THROUGH ALTERNATIVE PRODUCTION PRACTICES AND MANAGEMENT STRATEGIES: DISCUSSION

Farm Management, Risk and Uncertainty,

Cram\'{e}r-type large deviations for samples from a finite population

Cram\'{e}r-type large deviations for means of samples from a finite population are established under weak conditions. The results are comparable to results for the so-called self-normalized large deviation for independent random variables. Cram\'{e}r-type large deviations for the finite population Student $t$-statistic are also investigated.Comment: Published at http://dx.doi.org/10.1214/009053606000001343 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Senioritis in repose

Media and other accounts of life after retirement suggest it to be “The Golden Years” of life, when the elderly have true leisure in the classic sense of freedom from responsibilities of work. However, like earlier time-diary studies, data from the 2003-07 Americans Time Use Project (ATUS) indicate that the great majority of seniors’ extra 20+ hours of free time is concentrated on three activities – TV, reading and rest. Only a few more hours are spent on sleep. Despite reports of increased work time among seniors, relatively few of those in Andy’s new age bracket remain in the labor force and they work fewer hours.Time use, elderly, retirement, free time, TV, aging