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In this paper, we propose a new framework to construct confidence sets for a |$d$| -dimensional unknown sparse parameter |${\boldsymbol \theta }$| under the normal mean model |${\boldsymbol X}\sim N({\boldsymbol \theta },\sigma ^{2}\bf{I})$|⁠. A key feature of the proposed confidence set is its capability to account for the sparsity of |${\boldsymbol \theta }$|⁠ , thus named as sparse confidence set. This is in sharp contrast with the classical methods, such as the Bonferroni confidence intervals and other resampling-based procedures, where the sparsity of |${\boldsymbol \theta }$| is often ignored. Specifically, we require the desired sparse confidence set to satisfy the following two conditions: (i) uniformly over the parameter space, the coverage probability for |${\boldsymbol \theta }$| is above a pre-specified level; (ii) there exists a random subset |$S$| of |$\{1,...d\}$| such that |$S$| guarantees the pre-specified true negative rate for detecting non-zero |$\theta _{j}$| 's. To exploit the sparsity of |${\boldsymbol \theta }$|⁠ , we allow the confidence interval for |$\theta _{j}$| to degenerate to a single point 0 for any |$j\notin S$|⁠. Under this new framework, we first consider whether there exist sparse confidence sets that satisfy the above two conditions. To address this question, we establish a non-asymptotic minimax lower bound for the non-coverage probability over a suitable class of sparse confidence sets. The lower bound deciphers the role of sparsity and minimum signal-to-noise ratio (SNR) in the construction of sparse confidence sets. Furthermore, under suitable conditions on the SNR, a two-stage procedure is proposed to construct a sparse confidence set. To evaluate the optimality, the proposed sparse confidence set is shown to attain a minimax lower bound of some properly defined risk function up to a constant factor. Finally, we develop an adaptive procedure to the unknown sparsity. Numerical studies are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Ensuring that ambiguity cycles are correctly fixed as integers is a critical prerequisite for ensuring the reliability of GNSS high-precision carrier positioning results. As a result, it is both theoretically and practically important to investigate the performance of the ambiguity validation test by selecting an appropriate threshold. To begin, two statistics are proposed in this paper to quantitatively describe the performance of the validation test, namely the true negative rate and the false positive rate, which are based on the percentage of Type I errors (discarded-truth) in the total number of failed tests and the percentage of Type II errors (false positive) in the total number of passed tests. Following that, this paper employs the false positive rate and the true negative rate as primary and secondary criteria for evaluating the performance of the R-ratio test, respectively, and develops simulation experiments to evaluate the performance of different thresholds under different ambiguity dimensions and data accuracy, and finally provides decisions for test threshold selection: (1) For ambiguities with 4 to 9 dimensions, a reference table for the selection of thresholds is given. (2) For ambiguities of 10 dimensions or more, the threshold value should be no less than 2.0 (where data with a mean value of more than 3.7 for the main diagonal elements of the variance matrix should not be fixed). [ABSTRACT FROM AUTHOR]

Hydraulic systems are advanced in function and level as they are used in various industrial fields. Furthermore, condition monitoring using internet of things (IoT) sensors is applied for system maintenance and management. In this study, meaningful features were identified through extraction and selection of various features, and classification evaluation metrics were presented through machine learning and deep learning to expand the diagnosis of abnormalities and defects in each component of the hydraulic system. Data collected from IoT sensor data in the time domain were divided into clusters in predefined sections. The shape and density characteristics were extracted by cluster. Among 2335 newly extracted features, related features were selected using correlation coefficients and the Boruta algorithm for each hydraulic component and used for model learning. Linear discriminant analysis (LDA), logistic regression, support vector classifier (SVC), decision tree, random forest, XGBoost, LightGBM, and multi-layer perceptron were used to calculate the true positive rate (TPR) and true negative rate (TNR) for each hydraulic component to detect normal and abnormal conditions. Valve condition, internal pump leakage, and hydraulic accumulator data showed TPR performance of 0.94 or more and a TNR performance of 0.84 or more. This study's findings can help to determine the stable and unstable states of each component of the hydraulic system and form the basis for engineers' judgment. [ABSTRACT FROM AUTHOR]

Background: Diagnostic reviews often include the sensitivity/specificity results of individual studies. A problem occurs when these data are pooled because the correlation between sensitivity and specificity is generally strongly negative, causing overestimation of the pooled results. The diagnostic odds ratio (DOR), defined as the odds of true positives vs. that of false positives, may avoid this problem. The aim of the study was to review the advantages and limitations of the DORs. Methods: A systematic review of 44 previously published diagnostic studies was used as an example. Results: DORs can be readily implemented in diagnostic research. Advantages include: (1) they adjust for the negative and curvilinear correlations between sensitivities and specificities, (2) they take account of the heterogeneity between studies with respect to the different thresholds chosen by the investigators in the original studies, and (3) it is easy to extend the model with covariates representing between-study differences in design. Limitations include: 1) the outcome parameter is a summary estimate of both sensitivity and specificity, and 2) the magnitude of the studies included is not taken into account. Conclusions: Reported sensitivities and specificities of different studies assessing similar diagnostic tests are not only negatively correlated, but also negatively correlated in a curvilinear manner. It is appropriate to take this negative curvilinear correlation into account in the data pooling of such meta-analyses. The DORs can be applied for that purpose. Clin Chem Lab Med 2009;47:1351–4. [ABSTRACT FROM AUTHOR]