Variance Of Estimator Research Articles

Benchmarking performance in Targhee sheep in development of a genetic reference flock

Abstract The Targhee breed is important to range sheep production in the Western U.S. The objective of this research was to integrate industry sires participating in national genetic evaluation through the National Sheep Improvement Program (NSIP) into the U.S. Sheep Experiment Station (USSES) flock, where the breed originated, to benchmark sire performance. Estimated breeding values (EBV) of industry sires (n = 16) and USSES sires (n = 12) from the 2023 NSIP Targhee genetic evaluation differed (P < 0.05) only for the NSIP Number Born EBV. This difference, and small (nonsignificant) differences favoring industry sires for maternal weaning weight, yearling fiber diameter, and yearling staple length EBV also resulted in greater (P < 0.05) Western Range Index scores for industry sires. The performance of sires’ direct progeny born 2016 to 2018 was compared for 17 traits. After data cleaning, there were 664 progeny (417 from industry sires and 247 from USSES sires) with 146 to 664 records per trait. Least squares means differed (P < 0.05) for grease fleece weight, side fiber diameter, and britch fiber diameter in favor of the industry sires. Production traits were measured from the progeny and other retained descendants of both sire genetic groups from 2016 through 2022. After data cleaning, there was a range of 1,138 to 1,493 records per trait. A three-generation pedigree was constructed and the proportional assignment of each lamb to each genetic group (e.g., 0.5 industry, 0.5 USSES) was included in an augmented relationship matrix. A univariate animal model was fitted for each lamb trait and a repeated measures model for each of the three ewe traits was fitted to estimate variance components and predict breeding values. Genetic group solutions did not differ (P > 0.05) for any of these traits but provided a means by which to compare the two groups. Establishment of a Targhee genetic reference flock at USSES has been initiated, which can be used to address issues of importance to the industry.

Efficient designs for three-sequence stepped wedge trials with continuous recruitment.

The standard approach to designing stepped wedge trials that recruit participants in a continuous stream is to divide time into periods of equal length. But the choice of design in such cases is infinitely more flexible: each cluster could cross from the control to the intervention at any point on the continuous time-scale. We consider the case of a stepped wedge design with clusters randomised to just three sequences (designs with small numbers of sequences may be preferred for their simplicity and practicality) and investigate the choice of design that minimises the variance of the treatment effect estimator under different assumptions about the intra-cluster correlation. We make some simplifying assumptions in order to calculate the variance: in particular that we recruit the same number of participants, , from each cluster over the course of the trial, and that participants present at regularly spaced intervals. We consider an intra-cluster correlation that decays exponentially with separation in time between the presentation of two individuals from the same cluster, from a value of for two individuals who present at the same time, to a value of for individuals presenting at the start and end of the trial recruitment interval. We restrict attention to three-sequence designs with centrosymmetry - the property that if we reverse time and swap the intervention and control conditions then the design looks the same. We obtain an expression for the variance of the treatment effect estimator adjusted for effects of time, using methods for generalised least squares estimation, and we evaluate this expression numerically for different designs, and for different parameter values. There is a two-dimensional space of possible three-sequence, centrosymmetric stepped wedge designs with continuous recruitment. The variance of the treatment effect estimator for given and can be plotted as a contour map over this space. The shape of this variance surface depends on and on the parameter , but typically indicates a broad, flat region of close-to-optimal designs. The 'standard' design with equally spaced periods and 1:1:1 allocation rarely performs well, however. In many different settings, a relatively simple design can be found (e.g. one based on simple fractions) that offers close-to-optimal efficiency in that setting. There may also be designs that are robustly efficient over a wide range of settings. Contour maps of the kind we illustrate can help guide this choice. If efficiency is offered as one of the justifications for using a stepped wedge design, then it is worth designing with optimal efficiency in mind.

Robust and memory-less median estimation for real-time spike detection.

We propose a novel 1-D median estimator specifically designed for the online detection of threshold-crossing signals, such as spikes in extracellular neural recordings. Compared to state-of-the-art algorithms, our method reduces estimator variance by up to eight times for a given buffer length. Likewise, for a given estimator variance, it requires a buffer length that is up to eight times smaller. This results in three significant advantages: the footprint area decreases by more than eight times, leading to reduced power consumption and a faster response to non-stationary signals.

Estimation of population variance using optional randomized response technique model in the presence of measurement errors

Measurement errors are an important consideration in sample surveys. Neglecting their influence can give misleading and inaccurate results. In this paper, we propose three variance estimators using Optional Randomized Response Technique (ORRT) in the presence of measurement error. Performance of the proposed estimators are evaluated through a simulation study and a numerical example.

Noise assessment of cold atom interferometry gradiometry observations

Over the past few decades, the development of interferometric techniques utilizing cold atoms has significantly advanced, particularly in the realm of gravimetry. This paper explores the characterization of noise within atomic gradiometry systems, which is essential for enhancing measurement accuracy as new methodologies and tools are introduced. Specifically, we examine the noise components using advanced techniques such as least squares component estimation and Allan variance analysis. Applying these sophisticated methods to two distinct datasets, our results robustly indicate that white noise is the predominant and most resilient type of noise in gravity gradiometry measurements based on atomic interferometry, with variances of σP12=2.97×10−8 for dataset 1 and σP22=5.66×10−7 for dataset 2. The predominance of white noise simplifies the system dynamics and enhances the reliability of the estimation methods. Furthermore, our calculations yield an uncertainty in the gravity gradient resolution of σ Γ1 = 0.13 E (where 1 E = 10−9 s−2) and σ Γ2 = 3.55 E over time, underscoring the high precision achievable with current interferometric techniques.

Характеристики оценки частоты последовательности сверхширокополосных сигналов с неизвестными длительностями

The work synthesizes a quasi-likelihood algorithm for estimating the frequency of a coherent sequence of ultra-wideband quasi-radio signals with unknown duration against a background of white Gaussian noise. When synthesizing the frequency estimation algorithm, instead of an unknown duration, some of its expected value is used. Analytical expressions are obtained for the statistical characteristics of the frequency estimate of a sequence of ultra-wideband quasi-radio signals depending on the pulse duration detuning parameter. In particular, the dependence of the variance of the frequency estimate of a sequence of ultra-wideband quasi-radio signals on the signal-to-noise ratio is obtained for different values of the duration detuning and the number of sequence pulses. It has been established that the frequency estimate bias does not depend on the number of pulses in the sequence, and for large values of the narrowband parameter there is no frequency estimate bias. It is shown that the duration detuning has a significant impact on the characteristics of the frequency estimate of a sequence of ultra-wideband quasi-radio signals, while at large values of the narrowband parameter the obtained expressions coincide with the known expressions for the variance and bias of the frequency estimates of a sequence of narrow-band radio signals.

SeaTrack: Rethinking Observation-Centric SORT for Robust Nearshore Multiple Object Tracking

Nearshore Multiple Object Tracking (NMOT) aims to locate and associate nearshore objects. Current approaches utilize Automatic Identification Systems (AIS) and radar to accomplish this task. However, video signals can describe the visual appearance of nearshore objects without prior information such as identity, location, or motion. In addition, sea clutter will not affect the capture of living objects by visual sensors. Recognizing this, we analyzed three key long-term challenges of the vision-based NMOT and proposed a tracking pipeline that relies solely on motion information. Maritime objects are highly susceptible to being obscured or submerged by waves, resulting in fragmented tracklets. We first introduced guiding modulation to address the long-term occlusion and interaction of maritime objects. Subsequently, we modeled confidence, altitude, and angular momentum to mitigate the effects of motion blur, ringing, and overshoot artifacts to observations in unstable imaging environments. Additionally, we designed a motion fusion mechanism that combines long-term macro tracklets with short-term fine-grained tracklets. This correction mechanism helps reduce the estimation variance of the Kalman Filter (KF) to alleviate the substantial nonlinear motion of maritime objects. We call this pipeline SeaTrack, which remains simple, online, and real-time, demonstrating excellent performance and scalability in benchmark evaluations.

A forced optional randomized response model for estimating the proportion of sensitive attribute

The randomized response technique (RRT) is widely considered for estimating the sensitive attribute in sample surveys. Various randomized response methods have been formulated by the different researchers which provide suitable estimates and privacy protection to the respondents. In the present paper, a new randomized response technique is introduced for estimating a sensitive attribute by amalgamating forced answer strategy into optional RRT. The mean and variance of estimates of proportion of sensitive attribute and sensitivity level under proposed method are derived. The proposed procedure is found to be more efficient than the existing RRTs. The privacy of the respondents possessing the sensitive attribute is well protected under the proposed strategy. The superiority of the proposed procedure is established with the help of a numerical study.

A new modified estimator of population variance in calibrated survey sampling

In survey statistics, estimating and reducing population variation is crucial. These variations can occur in any sampling design, including stratified random sampling, where stratum weights may increase the variance of estimators. Calibration techniques, which use additional auxiliary information, can help mitigate this issue. This paper examines three calibration-based estimators—calibration variance, calibration ratio, and calibration exponential ratio estimators—within the framework of stratified random sampling. The study generates data from normal, gamma, and exponential distributions to test these estimators. Results demonstrate that the proposed calibration estimators offer more accurate estimates of population variance and outperform existing methods in estimating population variance under stratified random sampling, providing more accurate and reliable estimates.

Strata Design for Variance Reduction in Stochastic Simulation

Stratified sampling is one of the powerful variance reduction methods for analyzing system performance, such as reliability, with stochastic simulation. It divides the input space into disjoint subsets, called strata, to draw samples from each stratum. Partitioning the input space properly and allocating greater computational effort to crucial strata can help accurately estimate system performance with a limited computational budget. How to create strata, however, has yet to be thoroughly examined. Strata design faces the curse of dimensionality and data scarcity as the input dimension increases. We analytically derive the optimal stratification structure that minimizes the estimation variance for univariate problems. Further, reconciling the optimal stratification into decision trees, we devise a robust algorithm for multi-dimensional problems. Numerical experiments and a wind turbine case study demonstrate the superiority of the proposed method in terms of variance reduction, leading to computational efficiency and scalability.

Standard Errors for Calibrated Parameters

Abstract Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case, we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally, we develop tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model.

Double-loop importance sampling for McKean–Vlasov stochastic differential equation

This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with the solution to the d-dimensional McKean–Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a stochastic interacting P-particle system, which is a set of P coupled d-dimensional stochastic differential equations (SDEs). Importance sampling (IS) is a common technique for reducing high relative variance of MC estimators of rare-event probabilities. We first derive a zero-variance IS change of measure for the quantity of interest by using stochastic optimal control theory. However, when this change of measure is applied to stochastic particle systems, it yields a P×d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \ imes d$$\\end{document}-dimensional partial differential control equation (PDE), which is computationally expensive to solve. To address this issue, we use the decoupling approach introduced in (dos Reis et al. 2023), generating a d-dimensional control PDE for a zero-variance estimator of the decoupled SDE. Based on this approach, we develop a computationally efficient double loop MC (DLMC) estimator. We conduct a comprehensive numerical error and work analysis of the DLMC estimator. As a result, we show optimal complexity of OTOLr-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \ extrm{TOL}_{\ extrm{r}}^{-4}\\right) $$\\end{document} with a significantly reduced constant to achieve a prescribed relative error tolerance TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document}. Subsequently, we propose an adaptive DLMC method combined with IS to numerically estimate rare-event probabilities, substantially reducing relative variance and computational runtimes required to achieve a given TOLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{TOL}_{\ extrm{r}}$$\\end{document} compared with standard MC estimators in the absence of IS. Numerical experiments are performed on the Kuramoto model from statistical physics.

Initial trajectory parameters in the presence of range-Doppler coupling error

This paper focuses on obtaining our initial estimates for a Kalman filter. The Kalman filters are applied to estimate the motion parameters of objects detected by chirp radars. Chirp radars employ linear frequency modulated (LFM) waveforms for object tracking because the range-Doppler coupling allows better tracking accuracy in the range. The issues of initial trajectory parameters as a function of the range-Doppler coupling coefficient are discussed. Technically significant conditions of the same characteristics of the radar and the objects and equal deviations of the LFM signals in modulus at the moments of probing are used to form several measurements of the detected trajectory. Under the above conditions, there are 4 methods of determining the signs of the range-Doppler coupling coefficients for three measurements. The initial parameters of the trajectory for the second-order filter based on the three measurements are compared with each other at the methods of determining the signs of the range-Doppler coupling coefficients. The method l = 3 of determining the signs of the range-Doppler coupling coefficients (sign-variable the range-Doppler coupling coefficients) is advantageous because the normalized coordinates estimation variances take the smallest values compared to the other methods.

Imaging performance of a LaBr3:Ce scintillation detector for photon counting x-ray computed tomography: Simulation study.

Photon counting detectors (PCDs) for x-ray computed tomography (CT) are the future of CT imaging. At present, semiconductor-based PCDs such as cadmium telluride (CdTe), cadmium zinc telluride, and silicon have been either used or investigated for clinical PCD CT. Unfortunately, all of them have the same major challenges, namely high cost and limited spectral signal-to-noise ratio (SNR). Recent studies showed that some high-quality scintillators, such as lanthanum bromide doped with cerium (LaBr3:Ce), are less expensive and almost as fast as CdTe. The objective of this study is to assess the performance of a LaBr3:Ce PCD for clinical x-ray CT. We performed Monte Carlo simulations and compared the performance of 3 mm thick LaBr3:Ce and 2 mm thick CdTe for PCD CT with x-rays at 120 kVp and 20-1000mA. The two PCDs were operated with either a threshold-subtract (TS) counting scheme or a direct energy binning (DB) counting scheme. The performance was assessed in terms of the accuracy of registered spectra, counting capability, and count-rate-dependent spectral imaging-task performance, for conventional CT imaging, water-bone material decomposition, and K-edge imaging with tungsten as the K-edge material. The performance for these imaging-tasks was quantified by nCRLB, that is, the Cramér-Rao lower bound on the variance of basis line-integral estimation, normalized by the corresponding value of CdTe at 20mA. The spectrum recorded by CdTe was distorted significantly due to charge sharing, whereas the spectra recorded by LaBr3:Ce better matched the incident spectrum. The dead time, estimated by fitting a paralyzable detector model to the count-rate curves, was 20.7, 15.0, 37.2, and 13.0ns for CdTe with TS, CdTe with DB, LaBr3:Ce with TS, and LaBr3:Ce with DB, respectively. Conventional CT imaging showed an adverse effect of reduced geometrical efficiency due to optical reflectors in LaBr3:Ce PCD. The nCRLBs (a lower value indicates a better SNR) for CdTe with TS, CdTe with DB, LaBr3:Ce with TS, LaBr3:Ce with DB, and the ideal PCD, were 1.00±0.01, 1.00±0.01, 1.18±0.02, 1.18±0.02, and 0.79±0.01, respectively, at 20mA. The nCRLBs for water-bone material decomposition, in the same order, were 1.00±0.02, 1.00±0.02, 0.85±0.02, 0.85±0.02, and 0.24±0.02, respectively, at 20mA; and 0.98±0.02, 0.98±0.02, 1.09±0.02, 0.83±0.02, and 0.24±0.02, respectively, at 1000mA. Finally, the nCRLBs for K-edge imaging, the most demanding task among the five, were 1.00±0.02, 1.00±0.02, 0.55±0.02, 0.55±0.02, and 0.13±0.02, respectively, at 20mA; and 2.45±0.02, 2.29±0.02, 3.12±0.02, 2.11±0.02, and 0.13±0.02, respectively, at 1,000mA. The Monte Carlo simulations showed that, compared to CdTe with either TS or DB, LaBr3:Ce with DB provided more accurate spectra, comparable or better counting capability, and superior spectral imaging-task performances, that is, water-bone material decomposition and K-edge imaging. CdTe had a better performance than LaBr3:Ce for the conventional CT imaging task due to its higher geometrical efficiency. LaBr3:Ce PCD with DB scheme may be an excellent alternative option for CdTe PCD.

Spatial Ambiguity Correction in Coherence-Based Average Sound Speed Estimation.

Sound speed estimation can potentially correct the focusing errors in medical ultrasound. Maximizing the echo spatial coherence as a function of beamforming sound speed is a known technique to estimate the average sound speed. However, beamformation with changing sound speed causes a spatial shift of the echo signals resulting in noise and registration errors in the average sound speed estimates. We show that the spatial shift can be predicted and corrected, leading to superior sound speed estimates. Methods are presented for axial and 2-D location correction. Methods were evaluated using simulations and experimental phantom data. The location correction strategies improved the variance of sound speed estimates and reduced artifacts in the presence of strong backscatter variations. Limitations of the proposed methods and potential improvement strategies were evaluated.

Enabling Adaptive Sampling for Intra-Window Join: Simultaneously Optimizing Quantity and Quality

>Sampling is one of the most widely employed approximations in big data processing. Among various challenges in sampling design, sampling for join is particularly intriguing yet complex. This perplexing problem starts with a classical case where the join of two Bernoulli samples shrinks its output size quadratically and exhibits a strong dependency on the input data, presenting a unique challenge that necessitates adaptive sampling to guarantee both the quantity and quality of the sampled data. The community has made strides in achieving this goal by constructing offline samples and integrating support from indexes or key frequencies. However, when dealing with stream data, due to the need for real-time processing and high-quality analysis, methods developed for processing static data become unavailable. Consequently, a fundamental question arises: Is it possible to achieve adaptive sampling in stream data without relying on offline techniques? To address this problem, we propose FreeSam, which couples hybrid sampling with intra-window join, a key stream join operator. Our focus lies on two widely used metrics: output size, ensuring quantity, and variance, ensuring quality. FreeSam enables adaptability in both the desired quantity and quality of data sampling by offering control on the two-dimensional space spanned by these metrics. Meanwhile, adjustable trade-offs between quality and performance make FreeSam practical for use. Our experiments show that, for every 1% increase in latency limitation, FreeSam can yield a 3.83% increase in the output size while maintaining the level of the estimator's variance. Additionally, we give FreeSam a multi-core implementation and ensure predictability of its latency through both an analytic model and a neural network model. The accuracy of these models is 88.05% and 96.75% respectively.

Drill Hole Spacing Analysis for Evaluation of Quartz Sand Resources as Residual Material from On-Land Alluvial Tin Processing based on Global Estimation Variance and Kriging Variance, with Case Study in the Bangka and Belitung Islands, Indonesia

On-land alluvial tin mining activities produce residual materials from mineral processing or mineral washing; the major one of these is quartz sand, which can be utilized in the manufacturing industry. As time goes by, the reserves of alluvial tin are decreasing, which is in line with the increasing residual material from abundant mineral processing. Mining procedures are carried out following the Indonesian government regulations, covering mining as well as reprocessing. This motivated us to evaluate the potential of quartz sand at two mining sites in Bangka and Belitung Islands. This study evaluated alluvial tin processing residual quartz sand through drill hole spacing analysis (DHSA) by comparing two geostatistics parameters, namely global estimation variance (GEV) and kriging variance (KV). Drill hole samples were taken with varying spacing, ranging from 50 to 200 m, after which geostatistical analysis was carried out. With several simulations, the incorporation of GEV and KV was able to produce the optimal drill hole spacing with measured resource categories in the range of 40 to 55 m, indicated resources in the range of 55 to 85 m, and inferred resources >85 m. Accordingly, the total estimated quartz sand resources of both sites were obtained.

Machine learning to evaluate the relationship between social determinants and diabetes prevalence in New York City

IntroductionDiabetes is a leading contributor to cardiovascular disease and mortality; social determinants of health (SDOH) are associated with disparities in diabetes risk. Quantifying the cumulative impact of SDOH and identifying...

Efficiency of reversible MCMC methods: elementary derivations and applications to composite methods

Abstract We review criteria for comparing the efficiency of Markov chain Monte Carlo (MCMC) methods with respect to the asymptotic variance of estimates of expectations of functions of state, and show how such criteria can justify ways of combining improvements to MCMC methods. We say that a chain on a finite state space with transition matrix P efficiency-dominates one with transition matrix Q if for every function of state it has lower (or equal) asymptotic variance. We give elementary proofs of some previous results regarding efficiency dominance, leading to a self-contained demonstration that a reversible chain with transition matrix P efficiency-dominates a reversible chain with transition matrix Q if and only if none of the eigenvalues of $Q-P$ are negative. This allows us to conclude that modifying a reversible MCMC method to improve its efficiency will also improve the efficiency of a method that randomly chooses either this or some other reversible method, and to conclude that improving the efficiency of a reversible update for one component of state (as in Gibbs sampling) will improve the overall efficiency of a reversible method that combines this and other updates. It also explains how antithetic MCMC can be more efficient than independent and identically distributed sampling. We also establish conditions that can guarantee that a method is not efficiency-dominated by any other method.

The lack of causal link between myopia and intraocular pressure: Insights from cross-sectional analysis and Mendelian randomization study

ObjectiveThis study aimed to explore the potential causal relationship between intraocular pressure (IOP) and myopia. MethodsThe study included 3,459 patients who underwent corneal refractive surgery at our institution between 2021 and 2023. Preoperative data on IOP, spherical equivalent (SE), axial length (AL), and corneal thickness (CCT) were collected. The association between IOP and myopia was investigated through rank correlation analysis, and causal inference was examined using Mendelian randomization (MR) methods, including MR-Egger, weighted median, mode-based estimation, simple mode, and inverse variance weighted (IVW) approaches. Utilizing summary statistics from genome-wide association studies (GWAS), IOP was considered as the exposure, with myopia as the outcome variable. IVW method was employed for the primary analysis, supplemented by sensitivity analyses. ResultsCross-sectional analysis revealed a non-significant association between corrected IOP (cIOP) and myopia (r = -0.019, P = 0.12). MR analysis indicated a non-significant genetic causal relationship between cIOP and myopia under the IVW method (OR = 1.001; 95 % CI [0.999–1.003], P = 0.22), a finding corroborated in replication samples (OR = 0.98; 95 % CI [0.96–1.00], P = 0.099). ConclusionThis study did not find a direct causal link between IOP and the development of myopia. These findings challenge the traditional role attributed to IOP in the progression of myopia and highlight the complex, multifactorial process of myopia development. This provides a new perspective on understanding the intricate mechanisms behind myopia progression.