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Heteroskedasticity- and autocorrelation-robust (HAR) inference in time series regression typically involves kernel estimation of the long-run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test’s null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher-order expansions, we provide a unified size-power frontier for both kernel and weighted orthonormal series tests using nonstandard “fixed-b” critical values. We also provide a frontier for the subset of these tests for which the fixed-b distribution is t or F. These frontiers are respectively achieved by the QS kernel and equal-weighted periodogram. The frontiers have simple closed-form expressions, which show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.

Accuracy and speed of algorithms play an important role in the reconstruction of temperature field measurements by acoustic tomography. Existing algorithms are based on static models which only consider the measurement information. A dynamic model of three-dimensional temperature reconstruction by acoustic tomography is established in this paper. A dynamic algorithm is proposed considering both acoustic measurement information and the dynamic evolution information of the temperature field. An objective function is built which fuses measurement information and the space constraint of the temperature field with its dynamic evolution information. Robust estimation is used to extend the objective function. The method combines a tunneling algorithm and a local minimization technique to solve the objective function. Numerical simulations show that the image quality and noise immunity of the dynamic reconstruction algorithm are better when compared with static algorithms such as least square method, algebraic reconstruction technique and standard Tikhonov regularization algorithms. An effective method is provided for temperature field reconstruction by acoustic tomography.

In Global Navigation Satellite System (GNSS) positioning, gross errors seriously limit the validity of Kalman filtering and make the final positioning solutions untrustworthy. Thus, the detection and correction of gross errors have become indispensable parts of Kalman filtering. Starting by defining an incremental Chi-square method of recursive least squares, this paper extends this definition to Kalman filtering to detect gross errors, explains its nature and its relation with the currently adopted Chi-square variables of Kalman filtering in model and data spaces, and compares them with the predictive residual statistics. Two robust Kalman filtering models based on an incremental Chi-square method (CI-RKF) were established, and the one with a better incremental Chi-square component was selected based on a static accuracy evaluation experiment. We applied the selected robust model to the GNSS positioning and the GNSS/inertial measurement unit (IMU) / visual odometry (VO) integrated navigation experiment in an occluded urban area at the East China Normal University. We compared the results for conventional Kalman filtering (CKF) with a robust Kalman filtering constructed using predictive residual statistics and an Institute of Geodesy and Geophysics (IGGШ) weight factor, abbreviated as “PRS-IGG-RKF”. The results show that the overall accuracy of CI-RKF in GNSS positioning was improved by 22.68%, 54.33%, and 72.45% in the static experiment, and 12.30%, 7.50%, and 16.15% in the kinematic experiment. The integrated navigation results indicate that the CI-RKF fusion method increased the system positioning accuracy by 66.73%, 59.59%, and 59.62% in one of the severe occlusion areas, and 42.04%, 59.04%, and 52.41% in the other.

Motivated by biological interests in analyzing navigation behaviors of flying animals, we attempt to build a system measuring their motion states. To do this, in this paper, we build a vision system to detect unknown fast moving objects within a given space, calculating their motion parameters represented by positions and poses. We proposed a novel method to detect reliable interest points from images of moving objects, which can be hardly detected by general purpose interest point detectors. 3D points reconstructed using these interest points are then grouped and maintained for detected objects, according to a careful schedule, considering appearance and perspective changes. In the estimation step, a method is introduced to adapt the robust estimation procedure used for dense point set to the case for sparse set, reducing the potential risk of greatly biased estimation. Experiments are conducted against real scenes, showing the capability of the system of detecting multiple unknown moving objects and estimating their positions and poses.

Small satellites have limited payload and their attitudes are sometimes difficult to determine from the limited onboard sensors alone. Wrong attitudes lead to inaccurate map projections and measurements that require post-processing correction. In this study, we propose an automated and robust scheme that derives the satellite attitude from its observation images and known satellite position by matching land features from an observed image and from well-registered base-map images. The scheme combines computer vision algorithms (i.e., feature detection, and robust optimization) and geometrical constraints of the satellite observation. Applying the proposed method to UNIFORM-1 observations, which is a 50 kg class small satellite, satellite attitudes were determined with an accuracy of 0.02°, comparable to that of star trackers, if the satellite position is accurately determined. Map-projected images can be generated based on the accurate attitudes. Errors in the satellite position can add systematic errors to derived attitudes. The proposed scheme focuses on determining satellite attitude with feature detection algorithms applying to raw satellite images, unlike image registration studies which register already map-projected images. By delivering accurate attitude determination and map projection, the proposed method can improve the image geometries of small satellites, and thus reveal fine-scale information about the Earth.

We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.

We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points.We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.

Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M-estimation by down-weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on γ-divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum γ-divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, that is, it is automatically bias-corrected. These features make the proposed γ -logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation studies and the Pima data application are presented to demonstrate the performance of γ-logistic regression.

In this paper we focus on model risk and risk sensitivity when addressing the insurability of cyber risk. The standard statistical approaches to assessment of insurability and potential mispricing are enhanced in several aspects involving consideration of model risk. Model risk can arise from model uncertainty and parameter uncertainty. We demonstrate how to quantify the effect of model risk in this analysis by incorporating various robust estimators for key model parameters that apply in both marginal and joint cyber risk loss process modelling. Through this analysis we are able to address the question that, to the best of our knowledge, no other study has investigated in the context of cyber risk: is model risk present in cyber risk data, and how does is it translate into premium mispricing? We believe our findings should complement existing studies seeking to explore the insurability of cyber losses.

Let X be a centered random vector taking values in ℝ d and let Σ = 𝔼(X ⊗ X) be its covariance matrix. We show that if X satisfies an L₄ – L₂ norm equivalence (sometimes referred to as the bounded kurtosis assumption), there is a covariance estimator Σ̂ that exhibits almost the same performance one would expect had X been a Gaussian vector. The procedure also improves the current state-of-the-art regarding high probability bounds in the sub-Gaussian case (sharp results were only known in expectation or with constant probability). In both scenarios the new bounds do not depend explicitly on the dimension d, but rather on the effective rank of the covariance matrix Σ.