Coverage probability

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

On construction of the smallest one-sided confidence interval for the difference of two proportions

Abstract: For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at level $\alpha$ is obtained. A generalization of constructing the smallest one-sided confidence interval to other discrete sample spaces is discussed in the presence of nuisance parameters.

Bootstrap methods in nonparametric regression

Abstract: Bootstrap techniques naturally arise in the setting of nonparametric regression when we consider questions of smoothing parameter selection or error bar construction. The bootstrap provides a simple-to-implement alternative to procedures based on asymptotic arguments. In this paper we give an overview over the various bootstrap techniques that have been used and proposed in nonparametric regression. The bootstrap has to be adapted to the models and questions one has in mind. An interesting variant that we consider more closely is called the Wild Bootstrap. This technique has been used for construction of confidence bands and for comparison with competing parametric models.

On Various Confidence Intervals Post-Model-Selection

Abstract: We compare several confidence intervals after model selection in the setting recently studied by Berk et al. (2013), where the goal is to cover not the true parameter but a certain non-standard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the `naive' confidence interval, which is constructed as if the selected model were correct and fixed a-priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.

Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Abstract: Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine t...

Toward a Realistic Assessment of Multiple Antenna HCNs: Residual Additive Transceiver Hardware Impairments and Channel Aging

Abstract: Given the critical dependence of broadcast channels by the accuracy of channel state information at the transmitter (CSIT), we develop a general downlink model with zero-forcing precoding, applied in realistic heterogeneous cellular systems with multiple-antenna base stations (BSs) Specifically, we take into consideration imperfect CSIT due to pilot contamination, channel aging due to users relative movement, and unavoidable residual additive transceiver hardware impairments (RATHIs) Assuming that the BSs are Poisson distributed, the main contributions focus on the derivations of the upper bound of the coverage probability and the achievable user rate for this general model We show that both the coverage probability and the user rate are dependent on the imperfect CSIT and RATHIs More concretely, we quantify the resultant performance loss of the network due to these effects We depict that the uplink RATHIs have equal impact, but the downlink transmit BS distortion has a greater impact than the receive hardware impairment of the user Thus, the transmit BS hardware should be of better quality than user's receive hardware Furthermore, we characterise both the coverage probability and user rate in terms of the time variation of the channel It is shown that both of them decrease with increasing user mobility, but after a specific value of the normalized Doppler shift, they increase again Actually, the time variation, following the Jakes autocorrelation function, mirrors this effect on coverage probability and user rate Finally, we consider space-division multiple access (SDMA), single-user beamforming (SU-BF), and baseline single-input single-output transmission A comparison among these schemes reveals that the coverage by means of SU-BF outperforms SDMA in terms of coverage