Equivalent Estimates Research Articles

A note on simultaneous estimation of order restricted location parameters of a general bivariate symmetric distribution under a general loss function

The problem of simultaneous estimation of order restricted location parameters θ 1 and θ 2 ( − ∞ < θ 1 ≤ θ 2 < ∞ ) of a bivariate symmetric distribution, under a general loss function, is being considered. We unify many results proved in the literature by considering a general bivariate symmetric model and a quite general loss function. We use the Stein [Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Ann Inst Statist Math. 1964;16:155–160] and the Kubokawa [A unified approach to improving equivariant estimators. Ann Statist. 1994;22(1):290–299] techniques to derive estimators that improve upon the natural location equivariant estimator under a general loss function. We see that the improved Stein [Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Ann Inst Statist Math. 1964;16:155–160] type estimator is robust with respect to the choice of bivariate symmetric distribution and the loss function. It only requires the loss function to satisfy some generic conditions for providing improvement. A simulation study and a real-life data analysis are also carried out to validate the findings of the paper.

General Expression of Best Equivariant Estimators of Regression Coefficients in Seemingly Unrelated Regression Models

ABSTRACTSeemingly unrelated regression models have been commonly employed as regression models with multiple explanatory variables and multiple response variables having cross‐correlations. This paper discusses equivariant estimation of the regression coefficient vector and derives the best equivariant estimator under a generalized quadratic loss function. The result of this paper is shown to include the results of previous best equivariant estimators under specific loss functions as special cases.

Sustainability in Reconstructive Breast Surgery: An Eco-audit of the Deep Inferior Epigastric Perforator Flap Pathway.

The deep inferior epigastric perforator (DIEP) flap provides an effective and popular means for autologous breast reconstruction. However, with the complexity of the pathway, the environmental impact of the pathway has yet to be evaluated. A retrospective analysis of 42 unilateral DIEPs at a single reconstructive center was performed. Process mapping and life-cycle analyses were performed for equipment, staff, patients, and land. A bottom-up approach was adopted to calculate carbon dioxide equivalent estimates for the initial consultation, preoperative, intraoperative, and immediate postoperative periods. This study estimated the carbon footprint of a patient undergoing DIEP flap surgery to be approximately 233.96 kg CO2eq. Induction, maintenance, and running of anesthesia had the highest overall contribution to the carbon footprint (158.17 kg CO2eq, 67.60% overall). Patient and staff travel contributed more than 15% overall carbon emissions in this study. The impact of sterilization was less than half of that from waste management (0.81 versus 1.81 kg CO2eq, respectively). Waste management alone contributed 4.21 kg CO2eq of the overall carbon emissions, the majority of which was accountable to the incineration of 14.75 kg of noninfectious offensive waste. This study estimates the carbon footprint of the DIEP pathway. Strategies to mitigate the impact of carbon emissions including usage of reusable vs single-use equipment, virtual consultations, standardization of equipment packs, and optimizing waste disposal were suggested areas for improvement. Data from manufacturers on life-cycle assessments were limited, and further work is needed to fully understand and optimize the impact of DIEP surgery on the environment.

The first exit time of fractional Brownian motion from an unbounded domain

Consider a fractional Brownian motions starting at the interior point x0,h‖x0‖+2K∈Rd+1 with the constant K>1, for some fixed x0∈Rd, of an unbounded domain D=x,y∈Rd+1:y>h‖x‖, The function h is a nondecreasing, lower semicontinuous, and convex function on [0,∞) with h(0) being finite. Here we take h−1x=Axαlogxβwith a positive constant A for x>K. It is evident that h−1(x) exhibits monotonic behavior for sufficiently large values of x. Let τD denote the first time that the fractional Brownian motion exits from D. In most cases, we give the asymptotically equivalent estimate of logPτD>t. The proof methods are based on the earlier works of Li, Shi, Lifshits, and Aurzada.

Characterization of non-Gaussianity in the snow distributions of various landscapes

Abstract. Seasonal snowpack is an important predictor of the water resources available in the following spring and early-summer melt season. Total basin snow water equivalent (SWE) estimation usually requires a form of statistical analysis that is implicitly built upon the Gaussian framework. However, it is important to characterize the non-Gaussian properties of snow distribution for accurate large-scale SWE estimation based on remotely sensed or sparse ground-based observations. This study quantified non-Gaussianity using sample negentropy; the Kullback–Leibler divergence from the Gaussian distribution for field-observed snow depth data from the North Slope, Alaska; and three representative SWE distributions in the western USA from the Airborne Snow Observatory (ASO). Snowdrifts around lakeshore cliffs and deep gullies can bring moderate non-Gaussianity in the open, lowland tundra of North Slope, Alaska, while the ASO dataset suggests that subalpine forests may effectively suppress the non-Gaussianity of snow distribution. Thus, non-Gaussianity is found in areas with partial snow cover and wind-induced snowdrifts around topographic breaks on slopes and on other steep terrain features. The snowpacks may be considered weakly Gaussian in coastal regions with open tundra in Alaska and alpine and subalpine terrains in the western USA if the land is completely covered by snow. The wind-induced snowdrift effect can potentially be partitioned from the observed snow spatial distribution guided by its Gaussianity.

MAIA and Humphrey Perimetry Differ in Their Estimation of Homonymous Visual Field Defects.

To assess whether the Humphrey Visual Field Analyzer (HFA) and the Macular Integrity Assessment instrument (MAIA) provide equivalent estimates of visual deficit size, severity, and progression in cortically blinded participants. Reliable, monocular 10-2 HFA and MAIA fields were collected at baseline, and after a blind-field training intervention (n = 54) or no intervention (n = 6) in adult participants with occipital strokes. Binocular HFA and MAIA mean sensitivities (MS) were first computed, before creating binocular maps of visual sensitivity for each perimetry system to calculate deficit areas, using a unitary, published, less than 10 dB criterion to define blindness. We contrasted HFA/MAIA MS and deficit area at individual study visits, together with change in these measures between visits. At individual visits, MS and deficit areas were well-correlated, but there were systematic differences between machines, greater for the intact than impaired hemifields, with the MAIA overestimating areas of visual deficit relative to the HFA. Between visits, the two perimeters' assessment of change in MS was correlated, but change in the deficit area was not, despite good test reliability. Reliable HFA and MAIA tests produce well-correlated but systematically offset estimates of visual sensitivity and deficit area in patients with homonymous field defects, which can impact assessment of progression. Cortically blinded patients exhibited comparable changes in sensitivity (spontaneous and training induced) when assessed using Humphrey and fundus-controlled MAIA perimetry. However, the photopic vs. mesopic nature of these tests impacted participant performance and suggests that custom, machine-specific criteria are needed to comparably define blindness on both systems.

HeadCTDosi: A python-based automated calculation of head water equivalent diameter and size specific dose estimate based on AAPM 220 report

The aim of the current study is to propose an algorithm for the automated calculation of water-equivalent diameter (Dw) and size-specific dose estimate (SSDE) from clinical computed tomography (CT) images in head protocol context, a python-based algorithm was developed in order to execute an interface to read DICOM images and compute the mentioned metrics. All CT datasets were retrospectively acquired by the Siemens emotion 16 C T scanner. The algorithm developed in this study presents a novel approach for preprocessing and analyzing DICOM images obtained from head CT scans. Exploiting a custom Python script, the preprocessing pipeline begins with the conversion of pixel values to Hounsfield Units (HU) to ensure quantitative analysis accuracy. Subsequently, Gaussian filtering reduced noise while preserving essential features, followed by thresholding using Otsu's method for head region segmentation. Morphological operations refined the binary mask, which enhanced the method for contour detection via active contours. The outcome of this procedure is an accurate measurement of the head size metrics, including lateral (LAT) and anteroposterior (AP) dimensions, effective diameter (Deff), and water equivalent diameter (Dw). Statistical analyses are performed to derive mean statistics and compute SSDE using a conversion factor derived from Dw. Validation of the proposed algorithm used images of patients who had undergone head examination in a major pediatric university hospital. The proposed algorithm was compared to IndoseCT v20 b for Dw and SSDE calculations. The Dw values from HeadCTDosi were strongly correlated to those of IndoseCT by R2 = 0.97 and the SSDE values also presented high correlation of R2 = 0.93. This study presents an improved algorithm for calculating Dw and SSDE in the context of head CT, which notably can outperform the manual, subjective, and time-consuming process of contouring the head region, positioning it as a potentially essential tool for routine clinical dose monitoring.

Development of a novel automated algorithm for patient dosimetry in computed tomography: a step towards the facilitation of size-specific dose estimates and organs dosimetry estimations in a busy clinical workflow

Abstract Accurate dosimetry in computed tomography (CT) is essential for patient safety and effective radiation management. This study presents the development of an automated algorithm designed to enhance patient dosimetry by facilitating size-specific dose estimates (SSDE) and organ dose estimations. Utilizing a Python-based script, the proposed method integrates advanced image preprocessing, contour detection, and mathematical calculations to quantify key metrics from CT images. This automated approach addresses the limitations of manual measurement techniques. A retrospective analysis was conducted on CT axial images from examinations acquired with an 80-detector scanner. The algorithm processes DICOM images, converts pixel values to Hounsfield Units, applies Gaussian smoothing, windowing, and thresholding, followed by morphological operations to refine segmentation. It measures the water equivalent diameter (Dw) and estimates both region SSDE and organ doses, incorporating tissue attenuation. Validation was performed using an adult anthropomorphic ATOM phantom, with organ doses measured by optically stimulated luminescence dosimeters. The results demonstrated the algorithm’s potential in estimating SSDE and organ doses. Validation of the automated method revealed strong correlations for Dw and SSDE between the proposed method and manual measurements of five expert reviewers ranging from 0.86 to 0.99 for determination coefficient. Comparative analysis of organ doses showed close agreement between results from experimental setup against the proposed algorithm. The automated algorithm estimated brain dose with a mean of 21.8 mGy, while measurements from the ATOM phantom and CT Expo indicated 19.74 mGy and 23.05 mGy, respectively. For lung doses, the automated algorithm estimated 12.5 mGy compared to 11.0 mGy from the ATOM phantom and 13.1 mGy from CT Expo. Liver doses were measured at 12.7 mGy by the automated method, versus 12.1 mGy from the ATOM phantom and 11.1 mGy from CT Expo. This study shows the potential of automated image analysis techniques in enhancing dosimetry accuracy in CT examinations.

Cerebral and myocardial kinetics of [11C]acetoacetate and [11C]β-hydroxybutyrate: A comparative crossover study in healthy rats

BackgroundKetone metabolism has been studied using positron emission tomography (PET) with the radiotracers [11C]acetoacetate and [11C]β-hydroxybutyrate. However, whether these two radiotracers actually yield equivalent estimates of cerebral and myocardial ketone metabolism has not yet been investigated. This study aimed to investigate and compare the kinetics of both tracers in the brain and heart of healthy rats under varying levels of circulating ketones at baseline and after a single-dose exogenous ketone ester (KE) supplement. MethodsSix healthy Sprague-Dawley rats each underwent two scans with each tracer: one following oral KE administration and one with a placebo. Cerebral kinetic parameters (Ki, VT, and cerebral metabolic rate (CMR)) were obtained using the Patlak method, whereas myocardial kinetic parameters (K1, k2, and VT) were derived using a 1-tissue compartment model. Parameters were compared through mixed-effects, correlation, and Bland-Altman analyses. ResultsGlobal CMR increased 3–4-fold in the KE group versus placebo, with strong positive correlations between CMR and plasma ketone levels for both tracers. Correlations between [11C]acetoacetate and [11C]β-hydroxybutyrate were moderate and non-significant for relative cerebral uptake expressed as Ki (ρ = 0.40) and for VT (ρ = 0.38) but strongly positive for absolute uptake, CMR (r = 0.84), with a non-significant mean bias of −0.03. In contrast, myocardial kinetics showed only non-significant weak to moderate correlations between the radiotracers (K1 (r = 0.04), k2 (r = −0.27), and VT (ρ = 0.43)), with no systematic biases. Conclusion[11C]acetoacetate and [11C]β-hydroxybutyrate can be used interchangeably for measuring global CMR in healthy rats but differ in certain cerebral and myocardial kinetics. Whether these findings are generalizable to pathological conditions warrants further studies to explore the kinetics of these tracers in disease models.

Development of a mathematical model for harbor maneuvers to realize modeling automation

A simulation environment of harbor maneuvers is critical for developing automatic berthing. Mathematical models are widely used to estimate harbor maneuvers. However, user’s analysis and decision are necessary to derive, select, and identify the model because each actuator configuration needs an inherent mathematical expression. We proposed a new mathematical model for arbitrary configurations to overcome that issue. The new model is a hybrid model that combines the simplicity of the derivation of the Taylor expansion and the high degree of freedom of the MMG low-speed maneuvering model. We also developed a method to select mathematical expressions for the proposed model using system identification. Because the proposed model can easily derive mathematical expressions, we can generate multiple expressions simultaneously and choose the best one. This method can reduce the workload of model identification and selection. Furthermore, the proposed method will enable the automatic generation of mathematical models because it can reduce user’s decision-making and data analysis for the model generation due to its less dependency on the knowledge of ship hydrodynamics and captive model test. The proposed method was validated with free-running model tests and showed equivalent or better estimation performance than the conventional model generation method.

Distributed Bipartite Consensus of Multi-Agent Systems via Disturbance Rejection Control Strategy

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme.

Coordinated frequency control strategy for modern power system considering engagement willingness

The large scale integration of renewable energy sources (RES) is posing unprecedented challenges to the frequency stability of modern power systems, with system inertia being the primary concern. Under such a landscape, this paper introduces a coordinated control strategy aiming at enhancing frequency stability by swiftly adjusting the power output of flexible resources to mitigate power imbalances and further dampen frequency fluctuations. Firstly, a communication-free center of inertia (COI) frequency estimation method is proposed. An equivalent inertia estimation method tailored for modern power systems is then developed by exploiting the correlation between synchronous inertia and active power fluctuations. By integrating the COI frequency variation rate with the estimated equivalent inertia, the imbalance power is calculated and compensated through the proposed coordinated control strategy. In this work, two typical flexible resources including photovoltaic (PV) generation and electric vehicles (EVs) are modeled and integrated into the testing system in PSCAD/EMTDC. Considering the contradiction between maximizing generation profit and reducing power output to mitigate frequency variation, the Corporate Social Responsibility (CSR) of renewable Generation Companies (GENCOs) is modeled to sketch their willingness of engaging into frequency support. Moreover, the frequency modulation potential of EVs in both commercial and residential areas are quantified for practical implementation. The simulations results successfully validate the effectiveness of the proposed control strategy.

Supercritical Carbon Dioxide Mixing Loss Characteristics Near the Critical Point

Abstract This paper aims to study the mixing loss characteristic of sCO2 near the critical point and shed light on the non-ideal fluid effect on the mixing losses. As a simplified model of the mixing process in the trailing edge or tip leakage flow in turbomachines, a case of mixing in a constant area adiabatic duct involving two streams of parallel flows is studied by control volume analysis. Both perfect gas and non-ideal fluid calculations are carried out for comparisons. The isolated and coupled effects of the two mixing streams' temperature, velocity, and pressure differences on the loss are investigated. The study shows that non-ideal fluid mixing produces significantly higher losses when compared to the equivalent perfect gas estimation. It also reveals that the non-ideal fluid mixing loss is sensitive to the average thermodynamic states of the mixing streams. A significant variation of the mixing loss coefficient is reported if the static state of any of the two streams is near the critical point, which is mainly caused by the significant variation of the temperature gradient regarding the entropy along the isobar. The results also show that the change in the mixing loss due to the variation of one property difference between mixing streams is almost independent of the other property difference. The results from this simple case contribute to understanding the mixing loss behaviour differences between perfect gas and non-ideal fluids in sCO2 turbomachinery and hold significance for the development of mean-line models.

Statistically optimal firstorder algorithms: a proof via orthogonalization

Abstract We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$ (and possibly some labels ${\boldsymbol{y}}\in{\mathbb{R}}^{n}$) and would like to estimate a coefficient vector ${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by ${\boldsymbol{X}}$ or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix ${\boldsymbol{X}}$ is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as ‘Bayes AMP’). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to \infty $, $n/d\to \delta $, and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

Assessing the influence of dose modulation on water equivalent diameter estimation in pediatric head CT imaging

Pediatric head computed tomography (CT) scans necessitate precise determination of radiation dose to optimize image quality while minimizing patient exposure. This study explores the influence of head size variation on radiation dose and image quality using phantom and patients set, aiming to investigate the efficacy of Automatic Exposure Control (AEC) in dose modulation. Image noise and radiation dose were assessed using with and without AEC, maintaining a constant tube current of 180 mA. The correlation between CT dose index volume (CTDIvol) and water-equivalent diameter (Dw) was examined across 134 image sets, revealing an exponential relationship indicative of AEC's contribution to elevated radiation exposure in larger heads. Furthermore, a slice-based analysis demonstrated a consistent variation in tube current along the slice location, effectively modulated by Dw. However, discrepancies in tube current were observed in the caudal region, suggesting the influence of factors beyond section size. Refinement of analysis improved curve fitting, highlighting the importance of section size in dose modulation. AEC proved essential in maintaining image quality consistency across slices, with inactive AEC resulting in lower image noise in cranial slices. These findings highlight the significance of AEC-based dose modulation in pediatric head CT to ensure optimal image quality while minimizing radiation exposure, emphasizing the need for comprehensive understanding and implementation of AEC systems from different manufacturers.

Quantifying weather-induced unreliable public transportation service in cold regions under future climate model scenarios

Climate change, particularly in cold regions, significantly challenges public transportation systems. This study conducts a comprehensive analysis of weather patterns and public transit reliability in the context of climate change impacts. Leveraging advanced modeling techniques, including a ridge regression model for snow water equivalent data estimation and a long short-term memory (LSTM) based on recurrent neural network, the study aims to assess the reliability trends of the rapid transit system under various climate scenarios. The findings reveal that climate change in general increases weather-related delays in the Toronto transit system. The number of short delays decreased accordingly due to changes in winter temperatures but exacerbated long delays as the number of weather extremes increased. The LSTM model performed effectively in predicting delays, especially for the rapid transit system sensitive to weather variations. This study emphasizes the need for robust planning and interventions to increase the resilience of transit systems against climate change and highlights the importance of the integration of climate and extreme weather considerations into transportation management.

Multiple integer candidates ambiguity resolution: a unification ambiguity resolution algorithm

Among all the ambiguity resolution techniques, the Full Ambiguity Resolution (FAR), Partial Ambiguity Resolution (PAR) and Best Integer Equivariant (BIE) estimator are widely used. Although the researches have been done on the different classes of ambiguity resolution, we still hope to find the relationships among these specific algorithms. In this work, we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates. A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived. Then, we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution (MICAR) to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR (FAR) algorithm instead of BIE. In the experiments, we utilize the simulated data of GPS (Global Positioning System) + BDS (BeiDou Navigation Satellite System) + Galileo (Galileo navigation satellite system) to contrast the effects of MICAR and single candidate estimator, i.e., FAR. By taking the threshold of 5 cm at 95% confidence level as an example, MICAR accelerates the convergence process by about 3.0 min. When the positioning sequence converges, MICAR reduces the root mean square of the positioning error by 9.8% in horizontal directions and 3.5% in vertical direction, which is attributed to more fixed NL.

Using quartz OSL signals from SAR cycles for sediment provenance studies

Quartz optically stimulated luminescence (OSL) sensitivity is varied and related to Earth surface processes and, thus, it has been shown to be a useful tool for appraising sediment recycling and provenance investigations. These investigations are mainly based on OSL data purposely measured for sensitivity calculations. However, it has been recently shown that the relative sensitivity of the quartz OSL fast component (%BOSLF) from the first test dose (Tn) signal from an OSL dating measurement using the Single Aliquot Regenerative-dose (SAR) protocol can be used to discriminate sediment sources. Here, we investigate the possibility of characterizing %BOSLF for provenance purposes using not only Tn signals but all other OSL signals obtained over SAR protocol cycles from OSL dating measurements. We address the %BOSLF behaviour over SAR cycles (if conservative or not), the %BOSLF dependency on dose-size, differences between %BOSLF values given by natural/regenerative and test dose signals, and %BOSLF application for provenance studies. Quartz sand grains data from twenty Late Quaternary sediment samples, representing orogenic and cratonic sources and diverse depositional contexts from South America, Africa, and Asia, are included in the analysis. All calculations were performed using data that have been previously obtained for equivalent dose estimation. The key finding is that the averaged %BOSLF of all SAR signals was representative of the samples' characteristic sensitivity and could satisfactorily discriminate samples from known sources, mainly in the case of high-sensitivity samples. We could distinguish sediment source areas by averaging the %BOSLF of OSL signals from SAR natural/regenerative and test doses together. Likewise, laboratories worldwide could produce regional/global sediment provenance fingerprinting reference data using their dating measurements accumulated throughout the last decade.

Third‐Order Structure Functions of Zonal Winds in the Thermosphere Using CHAMP and GOCE Observations

AbstractWe use multi‐year observations of cross‐track winds (u) from the CHAllenging Minisatellite Payload (CHAMP) and the Gravity Field and Steady State Ocean Circulation Explorer (GOCE) to calculate third‐order structure functions in the thermosphere as a function of horizontal separation (s). They are computed using the mean (〈δu3〉) and the median and implemented over non‐polar satellite paths in both hemispheres. On height averages, 〈δu3〉 is shown to scale with s2 for s ≃ 80–1,000 km, in agreement with equivalent estimates in the lower atmosphere from aircraft observations. Conversely, follows an s3 power law for almost the whole s range, consistent with the two‐dimensional turbulence scaling law for a direct enstrophy cascade. These scaling laws appear independent of winds in distinct atmospheric regions. Furthermore, the functions are predominantly positive, indicating a preferential cyclonic motion for the wind.

Best Integer Equivariant Estimation Based on Unsupervised Machine Learning for GNSS Precise Positioning and Navigation in Complex Environments

Best Integer Equivariant Estimation Based on Unsupervised Machine Learning for GNSS Precise Positioning and Navigation in Complex Environments