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We develop measures of uncertainty, including model confidence sets and a LogP measure, for shrinkage model selection procedures. The measures are developed for linear models, generalized linear models, and generalized additive models. We study the theoretical and empirical properties of the proposed measures, and demonstrate how theses measures work by applying them to real-life problems.

The problems of point and interval estimation of powers of scale parameter (σ12c) have been considered when samples are available from two normal populations with a common mean. Maximum likelihood estimators (MLEs) and plug-in estimators using some of the popular estimators of the common mean have been proposed. A sufficient condition for improving affine equivariant estimators using the quadratic loss function is derived. Moreover, we propose several interval estimators, such as the asymptotic confidence interval, bootstrap confidence intervals, HPD credible interval, and intervals based on generalized pivot variables. Interestingly, some of the well-known estimators for the common mean have been used in constructing the generalized confidence intervals. A numerical comparison among all the proposed estimators has been made in terms of risk (in the case of point estimation) values using the quadratic loss function and coverage probabilities, and average lengths (in the case of interval estimation). Based on our simulation results, some recommendations are given for the use of the estimators. A real-life example has been considered to demonstrate the estimation methods.

We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given value in a general regression model. Previously, this large sample coverage probability could only be estimated by simulation. Our formula only requires the evaluation, by numerical integration, of either a double or a triple integral, irrespective of the dimension of this specified vector parameter. We illustrate the application of this formula to a confidence interval for the odds ratio of myocardial infarction when the exposure is recent oral contraceptive use, following a preliminary test where two specified interactions in a logistic regression model are zero. For this real-life data, we compare this large sample coverage probability with the actual coverage probability of this confidence interval, obtained by simulation.

Calibration of credible regions derived from under- or misspecified models is an important and challenging problem. In this paper, we introduce a scalar tuning parameter that controls the posterior distribution spread, and develop a Monte Carlo algorithm that sets this parameter so that the corresponding credible region achieves the nominal frequentist coverage probability.

We introduce expected coverage probability as a measure for constructing confidence intervals for the binomial proportion, π . We propose a model based confidence interval for π using the expected coverage probabilities of the Clopper-Pearson interval. The method provides intervals comparable or better than the alternative intervals, such as the Wilson, Agresti-Coull and Jeffreys intervals.

The Internet of Things (IoT) technology has broad application prospects, but for the large-scale decentralized deployment of IoT devices, energy supply and data collection are the two challenges faced by IoT applications. UAV-assisted backscatter communication (BackCom) has the advantages of fast deployment, strong flexibility, and high line-of-sight (LoS) probability. Combining UAV technology with IoT applications to construct the multi-UAV-assisted BackCom system can effectively solve IoT’s energy supply and data collection problems and effectively promote the development of IoT technology. In practical applications, factors such as node distribution and UAV deployment should be considered comprehensively. This paper uses the Matérn clustering process (MCP) to model the node distribution of hotspot clustering scenarios and studies the working mechanism of using a radio frequency (RF) source carried by UAV to supply energy to a backscatter device (BD) and collecting data generated by the BD using a backscatter receiver. The approximate distribution functions of BD harvesting energy, BD activation probability, and system average coverage probability are derived. The correctness of the theoretical derivation was verified through Monte Carlo simulation, and the effects of UAVs altitude, density, and transmission power on BD activation probability and system average coverage probability were analyzed. The effectiveness of the multi-UAV-assisted BackCom system in hotspot clustering scenarios was verified.

For a given confidence interval, the central value is more likely to be equal to the parameter than a boundary value is. However, when considering two null hypotheses with hypothesized values that are equal to these two values, neither of the hypotheses should be rejected, because both values are inside the interval. Here, we propose a method called the h-function method that can be used to identify any two values in an interval. The proposed method improves confidence intervals by modifying an approximate interval, including a point estimator, to be exact, and by refining an exact interval to be a subset of the previous interval. We demonstrate the proposed method by applying it to three data sets. Simulation results are given in the Supplementary Material.

Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + $\\frac{\\mathrm{c}}{\\mathrm{n}}$ ), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n -1/3 ). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.

The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology.

The rapid development of intelligent high-speed railways (HSRs) has significantly improved the transportation efficiency of modern transit systems, while also imposing higher bandwidth demands on mobile communication systems. Free-space optical (FSO) communication technology, as a promising solution, can effectively meet the high-speed data transmission requirements in intelligent HSR scenarios. In this paper, we consider an intelligent HSR system based on beamwidth-adaptive FSO communication and investigate the coverage performance of the system. Different from the circular cells used in traditional radio frequency wireless communication systems, this paper focuses on the coverage problem of narrow-strip-shaped cells in HSR systems based on FSO communication. When the transmitter emits a wide beam, the channel gain includes geometric loss, atmospheric attenuation, and atmospheric turbulence. When the transmitter emits a narrow beam, the channel gain includes pointing error, atmospheric attenuation, and atmospheric turbulence. To adapt the width of the transmitter’s beam, we propose a beamwidth-adaptive HSR system and a beamwidth-adaptive method. Furthermore, we derive closed-form expressions of the edge coverage probability (ECP) and the percentage of cell coverage area (CCA), where the ECP is the probability that the received signal-to-noise ratio at the cell edge is greater than or equal to a given threshold, and the percentage of CCA dictates the percentage of locations within a cell that are not in outage. The accuracy of the derived theoretical expressions is validated through Monte-Carlo simulations. The average relative error of the ECP between theoretical and simulation results is only 0.035%, and the corresponding error of the percentage of CCA is 0.087%. In addition, the impacts of factors such as cell diameter, transmission power, signal-to-noise ratio threshold, and weather visibility on coverage performance are also discussed.