Local differential privacy (LDP) involves users perturbing their inputs to provide plausible deniability of their data. However, this also makes LDP vulnerable to poisoning attacks. In this paper, we first introduce novel poisoning attacks for ranking estimation. These attacks are intricate, as fake attackers do not merely adjust the frequency of target items. Instead, they leverage a limited number of fake users to precisely modify frequencies, effectively altering item rankings to maximize gains. To tackle this challenge, we introduce the concepts of attack cost and optimal attack item (set), and propose corresponding strategies for kRR, OUE, and OLH protocols. For kRR, we iteratively select optimal attack items and allocate suitable fake users. For OUE, we iteratively determine optimal attack item sets and consider the incremental changes in item frequencies across different sets. Regarding OLH, we develop a harmonic cost function based on the pre-image of a hash to select that supporting a larger number of effective attack items. Lastly, we present an attack strategy based on confidence levels to quantify the probability of a successful attack and the number of attack iterations more precisely. We demonstrate the effectiveness of our attacks through theoretical and empirical evidence, highlighting the necessity for defenses against these attacks. The source code and data have been made available at https://github.com/LDP-user/LDP-Ranking.git.

Summary In this article, the statistical inference of a hybrid system with incomplete observed data is studied based on the adaptive type‐II progressive hybrid censored samples. It is assumed that the lifetime of the component in hybrid systems follows an identical Weibull distribution. The maximum likelihood estimates of the unknown parameters and reliability function are obtained by using the fixed‐point iteration method. Under general entropy loss function, the Bayesian estimates and the highest posterior density credible intervals of the unknown parameters and reliability function are derived using Markov Chain Monte Carlo method. In addition, the approximate confidence intervals and Bootstrap confidence intervals are constructed. Finally, Monte Carlo simulation study is carried out to illustrate the performances of two different point estimates and different confidence intervals.

Crop phenology is of critical importance to crop type classification, crop growth monitoring and yield prediction. Data smoothing is an inevitable procedure before extracting crop phenology from remote sensing data. This paper chose Guanzhong Plain in Shaanxi Province, China as the study area to investigate the impacts of the smoothing methods on the extraction of crop phenology. Results show that the double logistic function-fitting is better in describing the overall trend of crop dynamics while the Savitzky-Golay filter can retain more details in vegetation index time series. According to ground observation data, crop phenology retrieved from remote sensing data is not very consistent with the ground observations. However, as for the first growing season, crop phenology derived from the double logistic function-fitting smoothed data tended to closer to observations, and as for the second growing season, that from the Savitzky-Golay filter smoothed data provided better results.