Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Analysis of Nonlinear Regression Models: A Cautionary Note

Abstract: Regression models are routinely used in many applied sciences for describing the relationship between a response variable and an independent variable. Statistical inferences on the regression parameters are often performed using the maximum likelihood estimators (MLE). In the case of nonlinear models the standard errors of MLE are often obtained by linearizing the nonlinear function around the true parameter and by appealing to large sample theory. In this article we demonstrate, through computer simulations, that the resulting asymptotic Wald confidence intervals cannot be trusted to achieve the desired confidence levels. Sometimes they could underestimate the true nominal level and are thus liberal. Hence one needs to be cautious in using the usual linearized standard errors of MLE and the associated confidence intervals.

Evaluation of Two Methods to Estimate and Monitor Bird Populations

Abstract: Background Effective management depends upon accurately estimating trends in abundance of bird populations over time, and in some cases estimating abundance. Two population estimation methods, double observer (DO) and double sampling (DS), have been advocated for avian population studies and the relative merits and short-comings of these methods remain an area of debate. Methodology/Principal Findings We used simulations to evaluate the performances of these two population estimation methods under a range of realistic scenarios. For three hypothetical populations with different levels of clustering, we generated DO and DS population size estimates for a range of detection probabilities and survey proportions. Population estimates for both methods were centered on the true population size for all levels of population clustering and survey proportions when detection probabilities were greater than 20%. The DO method underestimated the population at detection probabilities less than 30% whereas the DS method remained essentially unbiased. The coverage probability of 95% confidence intervals for population estimates was slightly less than the nominal level for the DS method but was substantially below the nominal level for the DO method at high detection probabilities. Differences in observer detection probabilities did not affect the accuracy and precision of population estimates of the DO method. Population estimates for the DS method remained unbiased as the proportion of units intensively surveyed changed, but the variance of the estimates decreased with increasing proportion intensively surveyed. Conclusions/Significance The DO and DS methods can be applied in many different settings and our evaluations provide important information on the performance of these two methods that can assist researchers in selecting the method most appropriate for their particular needs.

Confidence intervals for estimating the population signal-to-noise ratio: a simulation study

Abstract: This paper considered several confidence intervals for estimating the population signal-to-noise ratio based on parametric, non-parametric and modified methods. A simulation study has been conducted to compare the performance of the interval estimators under both symmetric and skewed distributions. We reported coverage probability and average width of the interval estimators. Based on the simulation study, we observed that some of our proposed interval estimators are performing better in the sense of smaller width and coverage probability and have been recommended for the researchers.

Confidence intervals for the mean and a percentile based on zero-inflated lognormal data

Abstract: The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include...