Estimation Of Location Parameters Research Articles

Sky location of Galactic white dwarf binaries in space-based gravitational wave detection

Quickly localizing the identified white dwarf (WD) binaries is the basic requirement for the space-based gravitational wave (GW) detection. In fact, the amplitude of GW signals are modulated by the periodic motion of GW detectors on the solar orbit. The intensity of the observed signals is enhanced according to the observation time beyond a year to enhance a high signal to noise ratio (SNR). As data gap exists, the completeness of the data observed for a long time depends on filling gaps in the data. Actually, in a year period, the GW sources have a best observation orbit position of GW detectors, where the intensity of GW is maximum. Thus, the best positions can be searched for the verified GW sources of the sky map to enhance SNR too, which avoids filling data gaps. For the three arms response intensity of the GW signals changing more clearly with the location of the GW sources relative to the detector, the noises and the suppression of noise by time delay interferometer are ignored. As a verification case, the four WD binaries are chosen, whose best observation orbit positions of the GW detectors are related to the direction of WD binaries perpendicular to the detection arms. The two verification binaries: J0806 and V407 Vul are observed at the best orbit positions by TAIJI for the short time of 2 and 3 days respectively. The corresponding intensities of GWs are above the values of the TAIJI sensitivity curve, significantly. Location parameter estimation of the verification WD binaries are performed using the Metropolis–Hastings MCMC method. The confidence level of the parameters obtained in the best position is significantly several times higher than that in the worst position where the direction of WD binaries are almost parallel to the detection arms. Compared with a single detector, the network of two detectors improve slightly the accuracy of location of the verification binaries. These results imply that the searching of GW signals and parameter estimation of GW sources from the experimental data of the space-based mission do not ignore the orbit positions relevant to GW sources.

Retracted: Research on Localization Parameter Estimation and Algorithm in the Digital Television Terrestrial Broadcasting

Retracted: Research on Localization Parameter Estimation and Algorithm in the Digital Television Terrestrial Broadcasting

Neutrosophic ratio-type exponential estimators for estimation of population mean

The current work is one step in filling a large void in the research left by the advent of neutrosophic Statistics (NS), a philosophized variant of classical statistics (CS). The philosophy of NS deals with techniques for investigating data that is ambiguous, hazy, or uncertain. The traditional techniques of estimation utilizing auxiliary information work under specific determinate data, which in the case of neutrosophic data may lead to mistakes (over/ under-estimation). This study presents a generalized neutrosophic ratio-type exponential estimator (NRTEE) for estimating location parameters and achieving the lowest mean square error (MSE) possible for interval neutrosophic data (IND). The offered NRTEE helps to deal with the uncertainty and ambiguity of data. Unlike typical estimators, its findings are not single-valued but rather in interval form, which reduces the possibility of over-or under-estimation caused by single crisp outcomes and also increases the likelihood of the parameter dwelling in the interval. It improves the efficiency of the estimator since we have an estimated interval that contains the unknown value of the population mean with a minimal MSE. The suggested NRTEE’s efficiency is further addressed by utilizing real-life IND of temperature and simulations. A comparison is also performed to establish the superiority of the proposed estimator over the traditional estimators. The limits are calculated and discussed in cases when our suggested estimator is always efficient. The suggested estimator is the most efficient of all estimators and outperformed all others on both IND and classical data.

Two new Bayesian-wavelet thresholds estimations of elliptical distribution parameters under non-linear exponential balanced loss

The estimation of mean vector parameters is very important in elliptical and spherically models. Among different methods, the Bayesian and shrinkage estimation are interesting. In this paper, the estimation of p-dimensional location parameter for p-variate elliptical and spherical distributions under an asymmetric loss function is investigated. We find generalized Bayes estimator of location parameters for elliptical and spherical distributions. Also we show the minimaxity and admissibility of generalized Bayes estimator in class of We introduce two new shrinkage soft-wavelet threshold estimators based on Huang shrinkage wavelet estimator (empirical) and Stein’s unbiased risk estimator (SURE) for elliptical and spherical distributions under non-linear exponential-balanced loss function. At the end, we present a simulation study to test the validity of the class of proposed estimators and physicochemical properties of the tertiary structure data set that is given to test the efficiency of this estimators in denoising.

A note on asymptotics of the risk function under confidence region estimation in case of large samples of random size

The problem of optimal estimation of location and scale parameters of absolutely continuous distributions, by means of two-dimensional confidence regions based on L-statistics, is considered. The case, when the sample size is random and tends to infinity, is studied. The paper can be considered as a supplement to Zaigraev and Alama-Bućko (Metrika 81:283–305, 2018) in case of samples of random size.

Mixed Near-Field and Far-Field Sources Localization via Oblique Projection

This paper presents a novel mixed source localization algorithm based on high-order cumulant (HOC) and oblique projection techniques. To address the issue of lower accuracy in near-field source (NFS) localization compared to the far-field source (FFS) localization, the presented algorithm further enhances the accuracy of NFS localization. First, the FFS’s direction-of-arrival (DOA) estimate is acquired utilizing a multiple signal classification (MUSIC) spectral peak search. To classify mixed sources more effectively, we utilize the oblique projection technique, which can successfully prevent FFS information from influencing the estimation of NFS parameters. A HOC matrix with solely NFS DOA information is built by choosing array elements in a specific sequence. The estimation of the NFS DOA is then derived using the estimation of signal parameters via a rotational invariance technique (ESPRIT)-like algorithm. Finally, the NFS range is acquired by a MUSIC search. The performance of the presented algorithm is discussed in several aspects. Compared to existing matrix difference methods, the presented algorithm, which adopts the oblique projection method, achieves superior results in the separation of mixed sources. Without excessively increasing the computational complexity, it not only ensures the performance of localization parameter estimation for FFS but also estimates the NFS with higher precision. The numerical simulations attest to the superior performance of the presented algorithm.

Robust testing procedures for scale differences in paired data

Several statistical tests have been proposed in the literature to assess the difference between two scale parameters in paired data. If the location parameters of each sample are different, many of these test statistics are adjusted using the estimated location parameters. Then, the performance of the test statistics depends on the selection of the location estimators. In this study, the asymptotically distribution-free test based on the U-statistic, which does not depend on two location parameters, is constructed. The asymptotic normality and the asymptotic power of the proposed test are examined. Furthermore, the proposed test is compared with the existing tests in terms of Pitman's asymptotic relative efficiency. To improve the Type I error rate in the small sample size, the robust test procedure based on the percentile bootstrap is also proposed. Our simulation studies show that the Type I error rate of the proposed test is more controlled and robust than existing tests in many situations. Further, the empirical power of the proposed test is shown to be high for heavy-tailed or asymmetric distributions.

Analysis of Climatic Change through Comparing Methods of Statistical Estimation for Two-Parameter Gamma Distribution in Nigeria

In other to improve the ability of decisionmakers to prepare for and deal with the unforeseen circumstances resulting from climate change as consequences of precipitation fluctuations, extreme and torrential rainfall. It is important to provide a more complete understanding of the range and likelihood of rainfall patterns a location could receive using a probabilistic model whose parameters might complement or even replace such common measures as the mean, median, variance, minimum, maximum and quartile values as major descriptors of rainfall at such location. Daily precipitation totals can be approximated by the gamma distribution as it is bounded on the left at zero and positively skewed indicating an extended tail to the right which suit the distribution of daily rainfall and accommodate the lower limit of zero which constrains rainfall values. This paper presents the comparison between Maximum Likelihood Estimation (MLE) of closed & open form solutions and Method of Moment Estimation (MME) of location and scaling parameters of the twoparameter gamma distribution, the parameters were estimated using MME and MLE with their performance adjudged and the result obtained showed that the closedform solution of the MLE outperformed the open form solution and MME by comparing their estimates for the scaling parameter.

Joint localization and channel estimation in flow-assisted molecular communication systems

In this paper, we present a joint localization and channel parameter estimation method in the presence of signal-dependent noise and inter-symbol interference for diffusive molecular communication systems. The joint parameter estimation of the nanomachine can provide reliable communication in a generic diffusive molecular communication system. In particular, an iterative maximum likelihood estimation (MLE) approach for jointly estimating locations, flow velocity, and diffusion coefficient is carried out. The Cramer–Rao lower bound on the variance of channel parameters and location is derived. The normalized estimation error is marginally higher for unknown parameters case than that of some known parameters. The individual result (location estimation or channel parameters estimation) outperforms the existing methods.

Quantum scale estimation

Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology, since current practice focuses almost exclusively on the estimation of phase and location parameters. For given prior probability and quantum state, and using Bayesian principles, a rule to construct the optimal probability-operator measurement is provided. Furthermore, the corresponding minimum mean logarithmic error is identified. This is then generalised as to accommodate the simultaneous estimation of multiple scale parameters, and a procedure to classify practical measurements into optimal, almost-optimal or sub-optimal is highlighted. As a means of illustration, the new framework is exploited to generalise scale-invariant global thermometry, as well as to address the estimation of the lifetime of an atomic state. On a more conceptual note, the optimal strategy is employed to construct an observable for scale parameters, an approach which may serve as a template for a more systematic search of quantum observables. Quantum scale estimation thus opens a new line of enquire—the precise measurement of scale parameters such as temperatures and rates—within the quantum information sciences.

Constrained Stochastic Inventory Control Models for Multi-Item with Variable Demand

Constrained multi-item inventory system with variable demands are considered. The demand rates of five selected multi-item - Cowbell, Milo, SMA, Cerelac and Golden Morn were modeled as Weibull, Normal and Lognormal probability distributions respectively with the aid of chi-squared multinomial goodness-of-fit test. The respective probability distributions with estimated location parameters: 491.55, 536.92, 10.5, 2.1926 and 5.3103 were used as the basis of probabilistic inventory models to obtain dynamic EOQ for each item under each constraint subject to Kuhn, Karush and Tucker (KKT) conditions as against the use of simple averages in deterministic inventory models. The optimal values of these constraints: available warehouse space (124sq.ft), specified level of inventory (94 units), limited capital (76,671.52 naira) and number of orders (1/month) were obtained using the optimal EOQ values to establish optimal inventory level and constraints level/capacity for each item in order to avoid shortage or excess stock.

A risk-based approach to measuring population micronutrient status from blood biomarker concentrations.

BackgroundNutrient biomarkers and their definitive cut-offs are used to classify individuals as nutrient-deficient or sufficient. This determinism does not consider any uncertainty, and a probability approach, using biomarker distributions, is then preferable to define the risk of nutrition deficiency when in populations.MethodHealthy 1–19-year-old children and adolescents were selected from the Comprehensive National Nutrition Survey (CNNS), to obtain probability distributions of their retinol, zinc and vitamin B12, along with erythrocyte folate. Model-based estimates of location, scale and shape parameters of these distributions were obtained across ages. Subsequently, in the entire sample of 1–19 year old children of CNNS, the population risk of deficiency (PRD) which is average risk of deficiency in individuals in the population was computed, which is “of concern” when >50%. When individual risk of deficiency is >97.5% it is called “severe risk of deficiency” (SRD).ResultsIn the entire CNNS sample, the PRD of concern was low for serum retinol (3.6–8.2%), zinc (0–5.5%), and SRD of vitamin B12 and erythrocyte folate were 2.3–7.2% and 4.2–9.7%, respectively, across age and sex groups.ConclusionThis proposed method assesses the adequacy of nutrient exposures without relying on pre-defined deterministic biomarker cut-offs to define micronutrient deficiency and avoids errors in exposure assessment.

A Multipath-Aided Localization Method for MIMO-OFDM Systems via Tensor Decomposition

Wi-Fi indoor localization has witnessed an increasing interest, benefiting from its low cost, easy accessibility and wide deployment. However, its applications are often restricted due to harsh multipath propagation in indoor environments. In this letter, we propose a tensor-based localization algorithm that fully exploits the multipath components (MPCs) within the channel state information. We first formulate the location parameter estimation problem as a tensor decomposition problem and ensure the uniqueness by a preprocessing step. Then, a multipath-aided localization method is proposed to achieve high-accuracy localization via fusing time-difference-of-arrival and angle-of-arrival information from all MPCs. Experimental results show that the proposed method can provide a stable sub-meter-level localization performance in multipath environments.

A Target Localization Method based on Optimized Newton Algorithm for MIMO Radar

Target localization is one of the fundamental research topics in multiple input multiple output (MIMO) radar systems. In this paper, we focus on the localization parameter estimation including direction of departure (DoD), direction of arrival (DoA) and radar cross section (RCS) coefficients in monostatic MIMO radar systems. An optimized Newton algorithm is proposed to jointly estimate DoAs/DoDs and RCS coefficients. Its angle estimation performance outperforms traditional Capon, MUSIC and ESPRIT methods. The proposed localization algorithm also has great RCS coefficient estimation performance. Moreover, the joint estimation performance of the proposed optimized Newton algorithm is superior even with unknown target numbers and low sampling numbers. Simulation results verify the effectiveness of the proposed optimized Newton algorithm.

An Iterative Method for Parameter Estimation of the Three-Parameter Weibull Distribution Based on a Small Sample Size with a Fixed Shape Parameter

The three-parameter Weibull distribution is popular in reliability analysis. However, in the context of a small sample size, the issue of parameter estimation of the three-parameter Weibull distribution is difficult to address. If only a small sample size is available, a reasonable method is to empirically determine the shape parameter, and the emphasis is placed on location parameter estimation. This paper presents a theoretical model to establish the relationship between the location parameter, the minimal sample value, and the sample size. Moreover, an iterative method is proposed to estimate the Weibull location parameter and scale parameter with an empirical value for the shape parameter. Compared with the maximum likelihood method (MLE), the Weibull plot with the sample correlation coefficient and TL-moment, the proposed method can more effectively estimate the parameters of the three-parameter Weibull distribution.

Parametric estimation of location and scale parameters based on ranked set sampling with unequal set sizes

Ranked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE’s from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic.

Location Parameter Estimation of Moving Aerial Target in Space–Air–Ground-Integrated Networks-Based IoV

Estimating the location parameters of moving target is an important part of intelligent surveillance for the Internet of Vehicles (IoV). Satellite has the potential to play a key role in many applications of space–air–ground-integrated networks (SAGINs). In this article, a novel passive location parameter estimator using multiple satellites for the moving aerial target is proposed. In this estimator, the direct wave signals in reference channels are first filtered by a band-pass filter, followed by a sequence cancelation algorithm to suppress the direct-path interference and multipath interference. Then, the fourth-order cyclic cumulant cross ambiguity function (FOCCCAF) of the signals in the reference channels and the four-weighted fractional Fourier transform FOCCCAF (FWFRFT-FOCCCAF) of signals in the surveillance channels are derived. Using them, the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) are estimated and the distance between the target and the receiver and the velocity of the moving aerial target are estimated by using multiple satellites. Finally, the Cramer–Rao lower bounds of the proposed location parameter estimators are derived to benchmark the estimator. The simulation results show that the proposed method can effectively and precisely estimate the location parameters of the moving aerial target.

Comparing Methods of Estimation for Two-Parameter Gamma Distribution Using Rainfall Patterns in Nigeria

In other to improve the ability of decision-makers to prepare for and deal with the unforeseen circumstances resulting from climate change as consequences of precipitation fluctuations, extreme and torrential rainfall. It is important to provide a more complete understanding of the range and likelihood of rainfall patterns a location could receive using a probabilistic model whose parameters might complement or even replace such common measures as the mean, median, variance, minimum, maximum and quartile values as major descriptors of rainfall at such location. Daily precipitation totals can be approximated by the gamma distribution as it is bounded on the left at zero and positively skewed indicating an extended tail to the right which suit the distribution of daily rainfall and accommodate the lower limit of zero which constrains rainfall values. This paper presents the comparison between Maximum Likelihood Estimation (MLE) of closed & open form solutions and Method of Moment Estimation (MME) of location and scaling parameters of the two-parameter gamma distribution, the parameters were estimated using MME and MLE with their performance adjudged and the result obtained showed that the closed-form solution of the MLE outperformed the open form solution and MME by comparing their estimates for the scaling parameter.

Uncertainty reduction in matched field inversion using Gaussian Processes

Gaussian Processes have been shown to be an effective tool for predicting an acoustic field in the ocean at a densely populated virtual array. This property is employed in this work for pre-processing acoustic data before these are used for source localization and geoacoustic parameter estimation using matched-field inversion (MFI). The process increases the accuracy of MFI as uncertainty in the estimation process is reduced. Via the application of Gaussian Processes, the data are denoised and interpolated and the new, enhanced fields are used as input to MFI along with replicas calculated at the virtual receivers at which field predictions are made. Kernel functions, implicit in the implementation of Gaussian Processes, quantify the correlation among field values at neighboring spatial points. Employing different kernels, the approach is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional Bartlett MFI in source localization and geoacoustic inversion. [Work supported by ONR.]

Information-Theoretic Aspects of Location Parameter Estimation under Skew-Normal Settings.

In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter () estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds.