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Background Count time series (e.g., daily deaths) are a very common type of data in environmental health research. The series is generally autocorrelated, while the widely used generalized linear model is based on the assumption of independent outcomes. None of the existing methods for modelling parameter-driven count time series can obtain consistent and reliable standard error of parameter estimates, causing potential inflation of type I error rate. Methods We proposed a new maximum significant ρ correction (MSRC) method that utilizes information of significant autocorrelation coefficient ρ estimate within 5 orders by moment estimation. A Monte Carlo simulation was conducted to evaluate and compare the finite sample performance of the MSRC and classical unbiased correction (UB-corrected) method. We demonstrated a real-data analysis for assessing the effect of drunk driving regulations on the incidence of road traffic injuries (RTIs) using MSRC in Shenzhen, China. Moreover, there is no previous paper assessing the time-varying intervention effect and considering autocorrelation based on daily data of RTIs. Results Both methods had a small bias in the regression coefficients. The autocorrelation coefficient estimated by UB-corrected is slightly underestimated at high autocorrelation (≥ 0.6), leading to the inflation of the type I error rate. The new method well controlled the type I error rate when the sample size reached 340. Moreover, the power of MSRC increased with increasing sample size and effect size and decreasing nuisance parameters, and it approached UB-corrected when ρ was small (≤ 0.4), but became more reliable as autocorrelation increased further. The daily data of RTIs exhibited significant autocorrelation after controlling for potential confounding, and therefore the MSRC was preferable to the UB-corrected. The intervention contributed to a decrease in the incidence of RTIs by 8.34% (95% CI, -5.69–20.51%), 45.07% (95% CI, 25.86–59.30%) and 42.94% (95% CI, 9.56–64.00%) at 1, 3 and 5 years after the implementation of the intervention, respectively. Conclusions The proposed MSRC method provides a reliable and consistent approach for modelling parameter-driven time series with autocorrelated count data. It offers improved estimation compared to existing methods. The strict drunk driving regulations can reduce the risk of RTIs.

The corrections needed to realize integer ambiguity resolution-enabled precise point positioning (PPP-RTK) at a single-receiver user are often treated as if they are deterministic quantities. The present contribution aims to study and analyze the effect the neglected uncertainty of these corrections, which are subject to time delay, has on the PPP-RTK user ambiguity resolution and positioning performance. Next to the analyses of the estimation results, we emphasize their quality information and show to what extent the assumed positioning precision that the user is provided with differs from the minimum-variance counterpart under an incorrectly specified user stochastic model. We develop and present two alternatives to the fully populated error variance matrix of the PPP-RTK corrections that the user can reconstruct with limited information from the provider so as to properly weigh his corrected data and achieve close-to-optimal performance for high latencies. Supported by numerical results, our study demonstrates that the alternative variance matrices are sufficient enough for the user to obtain improved instantaneous PPP-RTK performance and a realistic precision description in the positioning domain.

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or α-quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one-sided quantile unbiasedness.

Mutually unbiased bases (MUBs) are essential tools in quantum information science, with applications in state tomography, quantum cryptography, and quantum error correction. In this work, we introduce a constructive framework for generating MUBs using linear bipermutive cellular automata (LBCAs). By leveraging the algebraic structure of generalized Pauli operators over finite fields, we show that disjoint families of LBCAs correspond to commuting sets of such operators (CSPOs), which, in turn, generate MUBs. This correspondence enables the systematic construction of complete or incomplete sets of MUBs, depending on the number of disjoint LBCAs available in a given dimension. We also provide algebraic conditions to verify disjointness and discuss how the finite dimensionality constrains MUB completeness. Our approach reinterprets classical combinatorial structures in a quantum setting, offering new computational pathways for exploring MUBs through discrete dynamical systems.

The two-level normal hierarchical model (NHM) has played a critical role in statistical theory for the last several decades. In this paper, we propose random effects variance estimator that simultaneously (i) improves on the estimation of the related shrinkage factors, (ii) protects empirical best linear unbiased predictors (EBLUP) [same as empirical Bayes (EB)] of the random effects from the common overshrinkage problem, (iii) avoids complex bias correction in generating strictly positive second-order unbiased mean square error (MSE) (same as integrated Bayes risk) estimator either by the Taylor series or single parametric bootstrap method. The idea of achieving multiple desirable properties in an EBLUP or EB method through a suitably devised random effects variance estimator is the first of its kind and holds promise in providing good inferences for random effects under the EBLUP or EB framework. The proposed methodology is also evaluated using aMonte Carlo simulation study and real data analysis.

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper, we derive an estimator that is unbiased when the random-effects model holds. We do the same for two more general structures. We study the usefulness of these estimators against others by simulation, the size of the t-test being the criterion. Our findings suggest that the choice of estimator hardly matters when the regressor has the same distribution over the clusters. But when the regressor is a cluster-specific treatment variable, the choice does matter and the unbiased estimator we propose for the random-effects model shows excellent performance, even when the clusters are highly unbalanced.

In optical communication systems, photons are lost due to the attenuation of the transmission medium. To efficiently implement quantum information protocols, we need to be able to precisely describe such processes. In this paper, we propose statistical methods to estimate the attenuation coefficient of the fiber link. By following the Beer–Lambert law, we utilize the properties of the exponential distribution to estimate the rate parameter based on observable data. In particular, we determine the explicit forms of unbiased estimators that are suitable for censored (truncated) sets of data. Moreover, we focus on minimum-variance methods that ensure a reliable estimation of the attenuation coefficient.

Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitraryshaped region with smooth boundaries. This problem has been discussed previously in Efron and Tibshirani [Ann. Statist. 26 (1998) 1687-1718], and a corrected p-value with second-order asymptotic accuracy is calculated by the two-level bootstrap of Efron, Halloran and Holmes [Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 13429-13434] based on the ABC bias correction of Efron [J. Amer. Statist. Assoc. 82 (1987) 171-185]. Our argument is an extension of their asymptotic theory, where the geometry, such as the signed distance and the curvature of the boundary, plays an important role. We give another calculation of the corrected p-value without finding the \"nearest point\" on the boundary to the observation, which is required in the two-level bootstrap and is an implementational burden in complicated problems. The key idea is to alter the sample size of the replicated dataset from that of the observed dataset. The frequency of the replicates falling in the region is counted for several sample sizes, and then the p-value is calculated by looking at the change in the frequencies along the changing sample sizes. This is the multiscale bootstrap of Shimodaira [Systematic Biology 51 (2002) 492-508], which is third-order accurate for the multivariate normal model. Here we introduce a newly devised multistep-multiscale bootstrap, calculating a third-order accurate p-value for the exponential family of distributions. In fact, our p-value is asymptotically equivalent to those obtained by the double bootstrap of Hall [The Bootstrap and Edgeworth Expansion (1992) Springer, New York] and the modified signed likelihood ratio of Barndorff-Nielsen [Biometrika 73 (1986) 307-322] ignoring O(n-3/2) terms, yet the computation is less demanding and free from model specification. The algorithm is remarkably simple despite complexity of the theory behind it. The differences of the p-values are illustrated in simple examples, and the accuracies of the bootstrap methods are shown in a systematic way.

HDFS heterogeneous clusters usually have multiple storage media at the same time. How to efficiently read and write file copies and reasonably use various storage media is a problem to be solved. Dynamically adjusting the number of copies is important in HDFS, which can solve the problem of accessing a large number of hot files at the same time and improve the efficiency of cluster services. A method is introduced to calculate the number of dynamic HDFS copies based on file access popularity in this paper. Firstly, an algorithm was proposed to predict file popularity based on the cuckoo search optimization Markov model. The unbiased grey model is used to predict the accessing file's popularity at the next moment according to the recent access of the file. The cuckoo search is used to optimize the Markov model, and the prediction error is corrected. Then, the calculation method of the number of copies is designed based on the prediction of the popularity of the file to be accessed and the availability of the node. The experiment shows that the proposed method has a high fitting degree with the actual value, and the MAPE is 3.08%, and it is the smallest, compared with several commonly used prediction models. In CloudSim4.0 simulation platform, multiple users write 10 files to the cluster at the same time, and the change number of copies is calculated according to the predicted value at the next moment, so as to improve the user access efficiency.

Small area estimation has long been a popular and important research topic due to its growing demand in public and private sectors. We consider here the basic area level model, popularly known as the Fay–Herriot model. Although much of current research is predominantly focused on second order unbiased estimation of mean squared prediction errors, we concentrate on developing confidence intervals (CIs) for the small area means that are second order correct. The corrected CI can be readily implemented, because it only requires quantities that are already estimated as part of the mean squared error estimation. We extend the approach to a CI for the difference of two small area means. The findings are illustrated with a simulation study.