Usual Estimator Research Articles

Estimation of sensitive trait proportion using Kuk’s randomized response model with auxiliary information

Different strategies have been developed in survey sampling to address the issue of missing observations and non response. Asking direct questions can be difficult in getting a real response. To get over this problem, we can utilize an indirect approach, such as the randomized response technique (RRT) which is frequently used to estimate the proportion of sensitive trait. In this work, when population level data on a non-sensitive auxiliary variable is available, we provide an enhanced class of estimators for sensitive traits. This class of estimators is based on a generalization of the well-known Kuk’s estimator and a usual difference estimator proposed by Diana and Perri (2009). We verify the findings with survey information obtained from the University of Wah in Pakistan and a data set previously utilized by Zaizai (2006).

Almost unbiased ridge estimator in Bell regression model: theory and application to plastic polywood data

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion.

Improved modeling for dark photon detection with dish antennas

A vector dark matter candidate, also known as dark photon, would induce an oscillating electric field through kinetic mixing. One detection strategy uses a spherical reflector to focus the induced emission at its center of curvature. First, we investigate the effects of diffraction in this type of experiment from an analytical standpoint, making use of the Kirchhoff integral theorem in the low-curvature dish limit. Next, we estimate the impact of mode matching, in the case of detection by a pyramidal horn antenna. We show that the expected signal intensity can be significantly reduced compared to usual estimates. Our method is applied to the reinterpretation of the SHUKET experiment data, the results of which are shown to be degraded by a factor of ∼50 due to both diffraction and mode matching. The analytical method allows optimizing some experimental parameters to gain sensitivity in future runs. Our results can be applied to any dish antenna experiment using a low-curvature reflector. Published by the American Physical Society 2024

Memory type general class of estimators for population variance under simple random sampling

With an emphasis on memory-type approaches, this study presents a class of estimators specifically designed for estimating population variation in simple random sampling (SRS). The term ‘memory-type’ pertaining to the use of exponentially weighted moving averages (EWMA) statistic for the estimation, which utilizes the current and past information in temporal surveys. The study provides expressions for the bias and mean square error (MSE) of these estimators and establishes conditions under which their efficiency represses the conventional and other memory-type estimators. The theoretical findings are reinforced through a comprehensive simulation study conducted on hypothetically sampled populations. Additionally, the effectiveness of the proposed estimators is demonstrated utilizing real-life population data. The findings of simulation and real data application show the superiority of the proposed memory type estimator over the existing usual and memory type estimators.

A new regularity criterion for the 3D tropical climate model involving partial velocity component in Lorentz space

In this paper, we find a new regularity criterion of the 3D tropical climate model in terms of one component of the barotropic velocity. Our criteria of the velocity field improve the previous result by Berti et al. Moreover, we extend the regularity criteria of the Lebesgue spaces to that of larger Lorentz spaces. The key of this paper is by using interaction between partial and usual estimate to get upper bound of velocities.

Computable error bounds for quasi-Monte Carlo using points with non-negative local discrepancy

Abstract Let $f:[0,1]^{d}\to{\mathbb{R}}$ be a completely monotone integrand as defined by Aistleitner and Dick (2015, Acta Arithmetica, 167, 143–171) and let points $\boldsymbol{x}_{0},\dots ,\boldsymbol{x}_{n-1}\in [0,1]^{d}$ have a non-negative local discrepancy (NNLD) everywhere in $[0,1]^{d}$. We show how to use these properties to get a non-asymptotic and computable upper bound for the integral of $f$ over $[0,1]^{d}$. An analogous non-positive local discrepancy property provides a computable lower bound. It has been known since Gabai (1967, Illinois J. Math., 11, 1–12) that the two-dimensional Hammersley points in any base $b\geqslant 2$ have NNLD. Using the probabilistic notion of associated random variables, we generalize Gabai’s finding to digital nets in any base $b\geqslant 2$ and any dimension $d\geqslant 1$ when the generator matrices are permutation matrices. We show that permutation matrices cannot attain the best values of the digital net quality parameter when $d\geqslant 3$. As a consequence the computable absolutely sure bounds we provide come with less accurate estimates than the usual digital net estimates do in high dimensions. We are also able to construct high-dimensional rank one lattice rules that are NNLD. We show that those lattices do not have good discrepancy properties: any lattice rule with the NNLD property in dimension $d\geqslant 2$ either fails to be projection regular or has all its points on the main diagonal. Complete monotonicity is a very strict requirement that for some integrands can be mitigated via a control variate.

Robust Regression Techniques for Multiple Method Comparison and Transformation.

A generalization of Passing-Bablok regression is proposed for comparing multiple measurement methods simultaneously. Possible applications include assay migration studies or interlaboratory trials. When comparing only two methods, the method boils down to the usual Passing-Bablok estimator. It is close in spirit to reduced major axis regression, which is, however, not robust. To obtain a robust estimator, the major axis is replaced by the (hyper-)spherical median axis. This technique has been applied to compare SARS-CoV-2 serological tests, bilirubin in neonates, and an in vitro diagnostic test using different instruments, sample preparations, and reagent lots. In addition, plots similar to the well-known Bland-Altman plots have been developed to represent the variancestructure.

Comparação das distribuições Normal, Logística, Laplace e t de Student para o erro experimental na descrição bayesiana do acúmulo de matéria seca de Allium sativum

ABSTRACT: This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matteraccumulation (TDMA) of Allium sativumas a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertzmodels that use student’s t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5.The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertzmodel fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even forvaried error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations.

Estimation of monotone α-quantile of past lifetime function with application

Abstract In many physical situations, it is reasonable to assume that the α-quantile of past life functions is increasing. In this study, we propose a new estimator for an increasing α-quantile of the past life function for right-censored data. We investigate the asymptotic properties of the new estimator and explore its weak and strong convergence. The simulation results show that the new estimator is consistent and outperforms the usual estimator from the literature. As an illustrative example, a time event from a data set of the Mayo Clinic study on primary biliary cirrhosis was analyzed.

Ameliorating the diagnostic power of combined shewhart-memory-type control chart strategies for mean

A great deal of research in statistical process control (SPC) involves the integration of different ideas to achieve the optimal detection of anomalies in the location parameter of a process. Likewise, the prime rationale of the combined (Shewhart-Memory-type) strategies is to promptly detect the shift of any size: small, moderate or large. An effort, along the same lines, is made to detect shifts in the mean of a normally distributed process. The usual difference estimator of the process mean instead of the sample mean is employed in the Mixed EWMA-Crosier CUSUM Combined Shewhart Mixed EWMA-CUSUM and Combined Shewhart Mixed EWMA-Crosier CUSUM charts to make their upgraded versions. This enhances the sensitivity of these charts against any shift size. The performance of the charts is appraised and compared with some notable charts of the same ilk, with reference to the average run length (ARL), relative average run length, extra quadratic loss and performance comparison index. An illustrative example is also provided.

Estimation for Markov Chains with Periodically Missing Observations

When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non‐parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first‐order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher‐order Markov chains.

Trends in Reported Calcium and Magnesium Intake from Diet and Supplements by Demographic Factors: National Health and Nutrition Examination Survey, 2003-2018

BackgroundCalcium and magnesium are important micronutrients necessary for normal body functioning. ObjectiveThe objective of the study was to approximate usual nutrient intakes and estimate proportion of adults meeting the Estimated Average Requirement (EAR) of calcium and magnesium from diet, and diet plus supplements (total intake). Trends in the proportion of adults meeting the EAR were estimated by sex, age, and race and ethnicity. DesignThe study utilized data from the National Health and Nutrition Examination Survey, a cross-sectional survey of a nationally representative sample of the US civilian and noninstitutionalized population. Participants and settingThe continuous National Health and Nutrition Examination Survey survey data from 2003-2004 through 2017-2018 for dietary intake, and 2007-2008 through 2017-2018 for total intake were analyzed. The study sample included men and women (not lactating/pregnant) ages 19 years and older with 2 reliable 24-hour dietary recalls and energy intake >500 to <6,000 kcal/day (N = 35 037). Main outcome measuresMean daily intake and trends of proportion of adults meeting/exceeding the EAR for calcium and magnesium were estimated. Statistical analyses performedThe National Cancer Institute’s method was used to calculate daily intakes for calcium and magnesium by demographic subgroups. SAS SURVEYMEAN and SURVEYFREQ procedures were used to estimate means ± SE for continuous variables and frequencies and percentages for categorical variables, and 2-sample t test for P values. Trends were estimated with National Cancer Institute’s Joinpoint trend analysis program. ResultsMean daily dietary calcium intake and proportions of adults meeting the EAR from both diet and supplements was lowest among women (859 mg [61.9%]), adults ages 71 years and older (865 mg [60.3%]) and non-Hispanic Black individuals (782 mg [48.6%]) compared with men, younger age groups, and other races and ethnicities. Magnesium intake reported from diet was lowest in adults ages 71 years and older (276 mg), whereas total magnesium intake and proportion of meeting the EAR from both diet and supplements was lowest in women (302 mg) and men (52%), respectively, adults ages 19 to 30 years (305 mg [48.5%]), and non-Hispanic Black individuals (274 mg [35.5%]). The trends in the proportion of women and non-Hispanic White adults meeting the EAR from total calcium intake decreased significantly (P < .05) by 2.9% and 2.0%, respectively. ConclusionsWomen and adults ages 71 years and older had the lowest reported mean daily dietary calcium intake and proportion meeting the EAR for calcium from diet and supplements. Men and adults ages 19 to 30 years had the lowest proportion meeting the EAR for magnesium from diet and supplements with adults ages 19 to 30 years also having the lowest reported total magnesium intake from diet and supplements. Non-Hispanic Black individuals had the lowest proportion of meeting the EARs for calcium and magnesium from reported total intake. The trends in the proportion of women and non-Hispanic White individuals meeting the EARs for calcium through total intake decreased over time and remained stable in other subpopulations and for magnesium.

Estimation of population mean using ranked set sampling in the presence of measurement errors

Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators.

Hybrid class of robust type estimators for variance estimation using mean and variance of auxiliary variable

This study is completed for the estimation of unknown population variance for the variable of mean and variance of interest. To accomplish this task, a new generalized class of robust kind of variance estimators proposed utilizing known descriptives of auxiliary variable, for example, Mid-range, Hodges-Lehmann Mean, Tri-mean, deciles mean, coefficient of skewness, interquartile range, first quartile, coefficient of kurtosis, semi-interquartile average, inter decile range and Mean, etc. These conventional measures of auxiliary variable improve the accuracy of the suggested class under simple random sampling without replacement (SRSWOR) scheme. The properties such as the bias, mean square errors (MSE), and least MSE of the suggested class are derived up to first order of approximation. The superiority conditions of the developed class of estimators over existing estimators are also made out theoretically. Finally, numerical representation is also completed for the motivations behind the article. The usual variance estimator is considered as a benchmark for comparing all considered estimators in numerical illustration. The results have been indicated that the suggested class is performing better than the usual variance estimator and all other thoughts about existing estimators.

Bayes estimator for the inequality-constrained regression model*

This article studies the Bayesian estimation of the inequality-constrained regression model under a balanced loss function. The usual Bayes estimator is often involved in some complex integrals and has no explicit expression, which causes the corresponding properties be difficult to describe. Based on the idea of linear Bayes method suggested by Rao (1973), the present paper constructs a linear Bayes estimator for the regression parameters without specify their specific prior distributions. It is proved that the proposed linear Bayes estimator outperforms the corresponding least squares estimator, and numerical simulations show that when there is collinearity in design matrix, the linear Bayes estimator performs better than the usual Bayes estimator.

Estimation of Gumbel Distribution Based on Ordered Maximum Ranked Set Sampling with Unequal Samples

Sample selection is one of the most important factors in estimating the unknown parameters of distributions, as it saves time, saves effort, and gives the best results. One of the challenges is deciding on a suitable distribution estimate technique and adequate sample selection to provide the best results in comparison with earlier research. The method of moments (MOM) was decided on to estimate the unknown parameters of the Gumbel distribution, but with four changes in the sample selection, which were simple random sample (SRS), ranked set sampling (RSS), maximum ranked set sampling (MRSS), and ordered maximum ranked set sampling (OMRSS) techniques, due to small sample sizes. The MOM is a traditional method for estimation, but it is difficult to use when dealing with RSS modification. RSS modification techniques were used to improve the efficiency of the estimators based on a small sample size compared with the usual SRS estimator. A Monte Carlo simulation study was carried out to compare the estimates based on different sampling. Finally, two datasets were used to demonstrate the adaptability of the Gumbel distribution based on the different sampling techniques.

Adaptive suboptimal control of some discrete-time plants with nonstochastic bounded disturbances

This paper deals with the adaptive suboptimal control of linear, discrete-time, time-invariant, minimum phase, scalar plants in the presence of nonstochastic bounded unmeasurable disturbances whose upper and lower bounds, which may be asymmetric, are assumed to be unknown a priori. Additional assumption is that an order of the difference equation describing the plant is known a priori. The distinguishing feature of the problem stated in this paper is that neither bounds on the unmeasured disturbances, nor bounds on an allowable region to which the unknown plant parameters belong are assumed to be known a priori. To solve this problem, adaptation procedures for the point and membership set estimation are utilized. The standard recursive procedure with adjustable dead zone is employed in order to derive the point estimates of unknown plant parameters together with the point estimate of time-invariant disturbance component. The size of this dead zone depends on the previous point estimate of the bounds on the time-varying disturbance component and also on a fixed suboptimality index chosen by the designer. The estimates generated by the point estimation procedure are directly exploited to derive the adaptive control law. The main idea advanced in this paper is that, instead of unknown a priori membership set of these parameters, their peculiar hypothetical a posteriori membership sets are designed via the use of the measured system’s signals together with the current point estimate of bounds on the time-varying disturbance component. Contrary to the usual membership set estimation approach, this set is updated if only it is discovered that the unknown parameter vector does not belong in reality to this set. To this end, a remarkable property of the point estimation procedure is utilized. Such an approach makes it possible to reconstruct this set and to update the previous estimate of the bounds on the time-varying disturbance component. The finite convergence of the adaptation procedures and also the ultimate boundedness of system’s signals are established. To demonstrate an efficiency of the adaptive controller and support the theoretical study, simulation results are presented.

Xenon photonuclear cross sections for the production of 123I radionuclide

A simple reliable theoretical model for the calculation of total photo-absorption cross sections by atomic nuclei has been presented and applied it to get the relevant data needed for the evaluation of the production rate of 123I radionuclide isotope. Since experimental measurements are not available, the model calculation represents the only source of information. The present results, based on an accurate model of nuclear structure, are in very good agreement with the observed photoabsorption cross sections of Te isotopes, which provide reliable cross sections for the neighboring Xe nuclei, where the usual simple estimates are clearly discordant.

Performance comparison between maximum likelihood estimation and variational method for estimating simple linear regression parameter

Variational estimation method is a deterministic approximation technique which involves Bayesian framework while giving a point estimate instead of the usual Bayesian interval estimation. The linear regression model, which has always been a popular model, can benefit from the implementation of variational estimation method. In this paper, the theoretical basis on why variational method can reduce overfitting in linear regression is reviewed. Based on the review, in theory, variational method is more robust to overfitting than MLE. This paper also performed a simulation study. The simulation is done in a manner such that the simulation represents the situation of predicting for new or hidden data. The simulation starts from generating random explanatory data and generates the appropriate response data based on linear regression equation. Then, the randomly generated data is used to estimate the linear regression parameters. The simulation is performed to compare the parameters estimation results from variational method with the method of MLE. The comparison is done using the estimation values and the squared differences between true parameters value and the estimates. Empirical findings show that both methods have relatively close estimate values. It can be seen as the simulation study concludes that both variational and ML yield rather close parameters estimates for simple linear regression case. The estimates closeness gets more obvious as the sample size grows. The study also found that Variational method has performs better in terms of parameters estimation in linear regression when the sample size is small or the data has large variance.

Estimation of monotone bivariate quantile inactivity time with medical applications

&lt;p&gt;In most lifetime models, the bivariate $ \alpha $-quantile inactivity time is a vector of increasing functions. A novel estimator of this vector was created and investigated under this assumption. It was expected that the application of this knowledge would improve the efficiency of the estimator. It was proven that the proposed estimator is consistent and converges weakly to a bivariate Gaussian process under a suitable transformation. A simulation study was conducted to compare the performance of the proposed estimator with that of the usual estimator. Finally, the application of the proposed estimator is illustrated by analyzing a dataset comprising the time to blindness in patients with diabetic retinopathy.&lt;/p&gt;