A Simulation Study of Predicting Flush Date

For Canada's boreal forest region, the accurate modelling of the timing of the appearance of aspen leaves is important to forest fire management, as it signifies the end of the spring fire season that occurs after snowmelt. This article compares two methods, a midpoint rule and a conditional expectation method used to estimate the true flush date for interval-censored data from a large set of fire-weather stations in Alberta, Canada. The conditional expectation method uses the interval censored kernel density estimator of Braun et al. (2005 Braun , J. , Duchesne , T. , Stafford , J. E. ( 2005 ). Local likelihood density estimation for interval censored data . Canadian Journal of Statistics 33 : 39 – 60 .[Crossref], [Web of Science ®] , [Google Scholar]). The methods are compared via simulation, where true flush dates were generated from a normal distribution and then converted into intervals by adding and subtracting exponential random variables. The simulation parameters were estimated from the data set and several scenarios were considered. The study reveals that the conditional expectation method is never worse than the midpoint method, and that there is a significant advantage to this method when the intervals are large. An illustration of the methodology applied to the Alberta data set is also provided.     

Transformed Logit Confidence Intervals for Small Populations in Single Capture–Recapture Estimation

The good performance of logit confidence intervals for the odds ratio with small samples is well known. This is true unless the actual odds ratio is very large. In single capture–recapture estimation the odds ratio is equal to 1 because of the assumption of independence of the samples. Consequently, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture–recapture estimation. It is found that the transformed logit interval, after adding .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for the other capture–recapture confidence intervals proposed in statistical literature. Thus, given that the .5 transformed logit interval is very simple to compute and has a good performance, it is appropriate to be implemented by most users of the single capture–recapture method.     

Modifications of the Empirical Likelihood Interval Estimation with Improved Coverage Probabilities

The empirical likelihood (EL) technique has been well addressed in both the theoretical and applied literature in the context of powerful nonparametric statistical methods for testing and interval estimations. A nonparametric version of Wilks theorem (Wilks, 1938 Wilks , S. S. ( 1938 ). The large-sample distribution of the likelihood ratio for testing composite hypotheses . Annals of Mathematical Statistics 9 : 60 – 62 .[Crossref] , [Google Scholar]) can usually provide an asymptotic evaluation of the Type I error of EL ratio-type tests. In this article, we examine the performance of this asymptotic result when the EL is based on finite samples that are from various distributions. In the context of the Type I error control, we show that the classical EL procedure and the Student's t-test have asymptotically a similar structure. Thus, we conclude that modifications of t-type tests can be adopted to improve the EL ratio test. We propose the application of the Chen (1995 Chen , L. ( 1995 ). Testing the mean of skewed distributions . Journal of the American Statistical Association 90 : 767 – 772 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) t-test modification to the EL ratio test. We display that the Chen approach leads to a location change of observed data whereas the classical Bartlett method is known to be a scale correction of the data distribution. Finally, we modify the EL ratio test via both the Chen and Bartlett corrections. We support our argument with theoretical proofs as well as a Monte Carlo study. A real data example studies the proposed approach in practice.     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

Reduced-Variance Methods for Detectability Correction of Population Abundance

Detectability issues create uncertainty in field surveys of animal and plant populations. Detectability correction is one method employed to deal with this problem when there is reasonable certainty that detectability is roughly constant with time or in different areas. Two new reduced-variance estimators of detectability are introduced and evaluated for the case of using a detectability correction for new areas that are surveyed only once. The new estimates are unbiased or nearly unbiased and produce population estimates with smaller variance than the Lincoln–Petersen estimate.     

Sample Size Calculation and Blinded Sample Size Recalculation in Clinical Trials Where the Treatment Effect is Measured by the Relative Risk

In clinical trials with binary endpoints, the required sample size does not depend only on the specified type I error rate, the desired power and the treatment effect but also on the overall event rate which, however, is usually uncertain. The internal pilot study design has been proposed to overcome this difficulty. Here, nuisance parameters required for sample size calculation are re-estimated during the ongoing trial and the sample size is recalculated accordingly. We performed extensive simulation studies to investigate the characteristics of the internal pilot study design for two-group superiority trials where the treatment effect is captured by the relative risk. As the performance of the sample size recalculation procedure crucially depends on the accuracy of the applied sample size formula, we firstly explored the precision of three approximate sample size formulae proposed in the literature for this situation. It turned out that the unequal variance asymptotic normal formula outperforms the other two, especially in case of unbalanced sample size allocation. Using this formula for sample size recalculation in the internal pilot study design assures that the desired power is achieved even if the overall rate is mis-specified in the planning phase. The maximum inflation of the type I error rate observed for the internal pilot study design is small and lies below the maximum excess that occurred for the fixed sample size design.     

Bayes Estimation Based on Joint Progressive Type II Censored Data Under LINEX Loss Function

In the lifetime experiments, the joint censoring scheme is useful for planning comparative purposes of two identical products manufactured coming from different lines. In this article, we will confine ourselves to the data obtained by conducting a joint progressive Type II censoring scheme on the basis of the two combined samples selected from the two lines. Moreover, it is supposed that the distributions of lifetimes of the two products satisfy in a proportional hazard model. A general form for the distributions is considered, and we tackle the problem of obtaining Bayes estimates under the squared error and linear-exponential (LINEX) loss functions. As a special case, the Weibull distribution is discussed in more detail. Finally, the estimated risks of the various estimators obtained are compared using the Monte Carlo method.     

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

In this article, four bivariate exponential (BVE) distributions with subject to right censoring samples are presented. Bayesian estimates of the parameters of BVE are obtained through Linex and quadratic loss functions. Gamma prior distribution has been suggested to reforming the posterior function. The estimations and standard errors of parameters have also been obtained through simulation method. Markov chain Monte Carlo (MCMC) method is employed for the case of Block-Buse bivariate distribution because there was no closed form for estimator criteria. Simulation studies have been conducted to show that the computation parts can be implemented easily and comparing the estimated values due to two methods and with the true values as well.     

Variable Selection in Joint Location and Scale Models of the Skew-t-Normal Distribution

Variable selection is an important issue in all regression analysis, and in this article, we investigate the simultaneous variable selection in joint location and scale models of the skew-t-normal distribution when the dataset under consideration involves heavy tail and asymmetric outcomes. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. These estimators are compared by simulation studies.     

Testing parallelism of regression lines against ordered alternatives

For the problem of testing the equality of slopes of several regression lines against the alternative that the slopes are in increasing (decreasing) order of magnitude, two types of tests are proposed. These are the likelihood ratio test and a test that depends on suitable linear combination of one group statistics. Rank analogues of the two tests are also examined.