Estimation Of Location Parameters Research Articles

Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.

On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation based on the convergence point of blurring process is more robust and often more efficient than that of nonblurring process.

Equivariant Estimation of Common Location Parameter of Two Exponential Populations Using Censored Samples

In this paper, we consider the problem of estimating common location parameter of two exponential populations using type-II censored sam- ples when the scale parameters are unknown. The loss function is taken as the quadratic loss. First, we derive a class of a ne equivariant esti- mators, which includes the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). A suf- cient condition for improving estimators in the class is derived. Con- sequently, estimators dominating the MLE and the UMVUE in terms of the risk values are obtained. An example is given to compute the estimates using our result. Finally a simulation study has been carried out to numerically compare the risk functions of all the estimators.

Robust estimation of location and concentration parameters for the von Mises–Fisher distribution

Robust estimation of location and concentration parameters for the von Mises–Fisher distribution is discussed. A key reparametrisation is achieved by expressing the two parameters as one vector on the Euclidean space. With this representation, we first show that maximum likelihood estimator for the von Mises–Fisher distribution is not robust in some situations. Then we propose two families of robust estimators which can be derived as minimisers of two density power divergences. The presented families enable us to estimate both location and concentration parameters simultaneously. Some properties of the estimators are explored. Simple iterative algorithms are suggested to find the estimates numerically. It is shown that the presented approaches can be utilised to estimate either the location or concentration parameter. A comparison with the existing robust estimators is given as well as discussion on difference and similarity between the two proposed estimators. A simulation study is made to evaluate finite sample performance of the estimators. We apply the proposed methods to a sea star dataset and discuss the selection of the tuning parameters and outlier detection.

Interpretation of the magnetic data from anomaly 2c of Soork iron ore using the combination of the Euler deconvolution and TDX filter

TDX is a balanced (normalized) version of the horizontal derivative filter and can recognize the edges of the shallow and deep bodies simultaneously. This filter is commonly used in the edge detection of potential field data. In this paper, we used combination of this balanced edge detection filter and Euler deconvolution to estimate source locations, without any priori information about the nature (structural index) of the source. The proposed methods are demonstrated on synthetic magnetic anomalies, and the inversion results show that the proposed methods can successfully estimate location parameters of the sources. We also applied the proposed methods to real magnetic data from Soork iron ore mine in Iran, and the inversion results estimated the proposed method are consistent with the results from exploratory drilling.

On Quantizer Design for Distributed Bayesian Estimation in Sensor Networks

We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions, it is optimal to partition the local sensors into groups, with all sensors within a group using the same quantization rule. When all the sensors use identical number of decision regions, use of identical quantizers at the sensors is optimal. When the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations, we show that binary quantizers at the local sensors are optimal under certain conditions. Based on these observations, we address the location parameter estimation problem and present our optimal quantizer design approach. We also derive the performance limit for distributed location parameter estimation under the Bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit. We corroborate this result using simulations. We then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations. Using counter-examples, we also show that the previous results do not hold in this setting of dependent observations and, therefore, identical quantizers are not optimal.

An item response theory analysis of the Psychological Inventory of Criminal Thinking Styles: comparing male and female probationers and prisoners.

An item response theory (IRT) analysis of the Psychological Inventory of Criminal Thinking Styles (PICTS) was performed on 26,831 (19,067 male and 7,764 female) federal probationers and compared with results obtained on 3,266 (3,039 male and 227 female) prisoners from previous research. Despite the fact male and female federal probationers scored significantly lower on the PICTS thinking style scales than male and female prisoners, discrimination and location parameter estimates for the individual PICTS items were comparable across sex and setting. Consistent with the results of a previous IRT analysis conducted on the PICTS, the current results did not support sentimentality as a component of general criminal thinking. Findings from this study indicate that the discriminative power of the individual PICTS items is relatively stable across sex (male, female) and correctional setting (probation, prison) and that the PICTS may be measuring the same criminal thinking construct in male and female probationers and prisoners.

Balanced horizontal derivative of potential field data to recognize the edges and estimate location parameters of the source

Edge detection is a common task in the interpretation of potential field data, and many edge detection filters are presented to accomplish this task, which are the functions composed by the first-order horizontal derivative and vertical derivative of potential field data, but we find that the edges recognized by the existing edge detection filters are bigger than the true edges. In this paper, we present the balanced horizontal derivative (BHD) edge detection filter, which uses the ratio of the first-order horizontal derivative to the second-order horizontal derivative to recognize the edges of the source, and the recognized edges by the BHD edge detection filter are more correct and are more insensitive to noise. We derive a linear equation based on the derivatives of the BHD to estimate the depth of the source, and we also present a normalized total horizontal derivative (NTHD) method to image the location of the source. We demonstrate the presented methods on synthetic potential field data, and the results show that the presented methods can provide the edges and location parameters of the sources correctly, and the BHD filter can display the edges more clearly and correctly. At last, we apply the presented methods to real potential field data, and the inversion results computed by the presented methods are in accord with the geology information.

An Improved Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

Maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for detecting changes in both process mean and process variability. In this paper, we propose an improved MaxEWMA control charts based on ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS) schemes for simultaneous detection of both increases and decreases in the process mean and/or variability, named MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. These MaxEWMA control charts are based on the best linear unbiased estimators of location and scale parameters obtained under ORSS and OIRSS methods. Extensive Monte Carlo simulations have been used to estimate the average run length and standard deviation of run length of the proposed MaxEWMA control charts. These control charts are compared with their counterparts based on simple random sampling (SRS), that is, MaxEWMA‐SRS and MaxGWMA‐SRS control charts. The proposed MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts are able to perform better than the MaxEWMA‐SRS and MaxGWMA‐SRS control charts for detecting shifts in the process mean and dispersion. An application to real data is provided to illustrate the implementation of the proposed MaxEWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.

Application of balanced edge detection filters to estimate the location parameters of the causative sources using potential field data

Balanced edge detection filters can recognize the edges of the shallow and deep bodies simultaneously, and are commonly used in the edge detection of potential field data. In this paper, we present using the balanced edge detection filters to estimate source locations, and derive two linear equations based on the balanced edge detection filters that can estimate the locations of the source without any priori information about the nature (structural index) of the source. The proposed methods are demonstrated on synthetic gravity anomalies, and the inversion results show that the proposed methods can successfully estimate location parameters of the sources. I also apply the proposed methods to real magnetic data, and the inversion results estimated by the proposed methods are consistent with the results estimated by the other similar method.

Estimation of Location and Scale Parameters in Two-Parameter Exponential Distribution Based on Ranked Set Sample

In this article, we are interested in simultaneous comparison of the location and scale estimators of a two-parameter exponential distribution based on simple random sample (SRS) and ranked set sample (RSS) by using generalized variance (GV). We suggest various RSS strategies to estimate the scale parameter. Their performances in terms of GV are compared with SRS strategy. Finally, we illustrate the minimum values of set size, n, based on RSS, which would result in smaller GV than that based on SRS.

Adaptive quantizers for estimation

This paper addresses a problem of location parameter estimation from multibit quantized measurements. An adaptive estimation algorithm using an adjustable quantizer is proposed. By using general results from adaptive algorithms theory, the asymptotic estimation performance is obtained and optimized through the quantizer parameters. Despite its very low complexity, it can be shown that the proposed algorithm is asymptotically optimal for estimating a constant parameter.The asymptotic performance for optimal quantizer parameters is shown to rapidly reach real-valued based estimation performance as the number of bits increases. In practice, 4-bit quantization appears to be enough for estimation purposes. It is also shown that the performance gap between the quantized and continuous cases is even smaller when the parameter varies according to a random walk (Discrete Wiener process with or without drift).

Gold-MUSIC: A Variation on MUSIC to Accurately Determine Peaks of the Spectrum

This paper presents a new way of accurately determining peaks of the MUSIC (“Multiple emitter location and signal parameter estimation,” R. O. Schmidt, IEEE Trans. Antennas and Propagation, vol. AP-34, no. 3, pp. 276-280, Mar. 1986) spectrum, here considered from the point of view of estimating the directions of arrival (DOAs) of narrowband signals. It can be used, with any smart antenna geometry and for any purpose where MUSIC is applicable. The MUSIC algorithm for DOA estimation evaluates the MUSIC spectrum for various angles and chooses the maxima or peaks as the angles of arrival. The values obtained depend on the interval at which the spectrum is evaluated. The coarser the interval, the less accurate are the results in case of MUSIC. To improve accuracy and not depend on the interval, Root-MUSIC (“Direction finding for diversely polarized signals using polynomial rooting,” A. J. Weiss and B. Friedlander, IEEE Trans. Signal Processing, vol. 41, no. 5, pp. 1893-1905, May 1993), which involves finding the roots of a polynomial, is available. However, Root-MUSIC is applicable, in its original form, only to uniform linear arrays (ULA). The gold-MUSIC algorithm proposed in this paper is a two-stage process. The first stage evaluates the objective function at coarse intervals and determines peaks followed by an iterative approach based on gold-section univariate (GSU) minimization (Algorithms for Minimization Without Derivatives, R. Brent, Englewood Cliffs, NJ, USA: Prentice-Hall, 1983) to find accurate values of the peaks. If the number of peaks found so far is equal to the number of estimated peaks, the algorithm stops with this first stage. The second stage is an iterative step for fine resolution using finer intervals around the peaks found so far for finding peaks that were missing in previous iterations. This paper, also presents a method, based on a partitioning algorithm for estimating the number of emitters. The performance of gold-MUSIC is described, including its advantages and comparison of time complexities for MUSIC, Root-MUSIC and gold-MUSIC. The proposed algorithm gives good results even when the number of snapshots is small. This gives it an additional computational advantage. It does not compromise on the resolving power of MUSIC.

A Two-Stage Procedure for the Removal of Batch Effects in Microarray Studies

The presence of different batches is routinely observed in microarray studies and is well known that non-biological variability potentially confounding biological differences is commonly related to such batches. The removal of these undesired effects for a non-biased inference is often accomplished either with normalization methods that do not take into account all the available information, or with models that rely on strong parametric assumptions. We have developed a new method for the batch effects removal, named ber, which is based on a two-stage procedure for the estimation of location and scale parameters. Batch effects and biological differences are estimated using a regression approach and bagging, therefore mild distributional assumptions are required. We have compared ber with other commonly employed methods and we have shown that ber can bring to a higher power in detecting differentially expressed genes. The application of ber to a real microarray study led to interpretable biological results. The method is implemented in the R package ber, available through CRAN repository.

Estimation of Location Parameter from Two Biased Samples

We consider a problem of estimating an unknown location parameter from two biased samples. The biases and scale parameters of the samples are not known as well. A class of non-linear estimators is suggested and studied based on the fuzzy set ideas. The new estimators are compared to the traditional statistical estimators by analyzing the asymptotical bias and carrying out Monte Carlo simulations.

Interpretation of magnetic anomalies by horizontal and vertical derivatives of the analytic signal

Magnetic anomalies are often disturbed by the magnetization direction, so we can’t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index (expressing the geometry) by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.

Inference for linear and nonlinear stable error processes via estimating functions

This paper describes an estimating function approach for parameter estimation in linear and nonlinear times series models with infinite variance stable errors. Joint estimates of location and scale parameters are derived for classes of autoregressive (AR) models and random coefficient autoregressive (RCA) models with stable errors, as well as for AR models with stable autoregressive conditionally heteroscedastic (ARCH) errors. Fast, on-line, recursive parametric estimation for the location parameter based on estimating functions is discussed using simulation studies. A real financial time series is also discussed in some detail.

Particle filtering for arrival time tracking in space and source localization

Locating and tracking a source in an ocean environment and estimating environmental parameters of a sound propagation medium are critical tasks in ocean acoustics. Many approaches for both are based on full field calculations which are computationally intensive and sensitive to assumptions on the structure of the environment. Alternative methods that use only select features of the acoustic field for localization and environmental parameter estimation have been proposed. The focus of this paper is the development of a method that extracts arrival times and amplitudes of distinct paths from measured acoustic time-series using sequential Bayesian filtering, namely, particle filtering. These quantities, along with complete posterior probability density functions, also extracted by filtering, are employed in source localization and bathymetry estimation. Aspects of the filtering methodology are presented and studied in terms of their impact on the uncertainty in the arrival time estimates. Using the posterior probability densities of arrival times, source localization and water depth estimation are performed for the Haro Strait Primer experiment; the results are compared to those of conventional methods. The comparison demonstrates a significant advantage in the proposed approach.

Estimation of the parameters of rayleigh distribution based on record values for censored data

In this paper, we discuss the estimation of location and scale parameters of the Rayleigh distribution based on the Upper record values by the best linear unbiased estimator (BLUE) and an alternative linear estimate, proposed by Gupta (1952). Type II singly and doubly censored samples are used for estimation. Tables of coefficients for best linear estimator and alternative estimator of are presented for various choices of censoring for n 8. Variances and covarinces of estimator of for BLUE and for alternative estimator are also presented. The computational formula and procedure used are explained. The purpose of the paper is to compare the performance of the estimation procedures in terms of relative efficiencies. The findings of the study suggest that the BLUE method can be replaced by Gupta method especially in the large samples.

A Decoupled Approach for Near-Field Source Localization Using a Single Acoustic Vector Sensor

This paper considers the problem of three-dimensional (3-D, azimuth, elevation, and range) localization of a single source in the near-field using a single acoustic vector sensor (AVS). The existing multiple signal classification (MUSIC) or maximum likelihood estimation (MLE) methods, which require a 3-D search over the location parameter space, are computationally very expensive. A computationally simple method previously developed by Wu and Wong (IEEE Trans. Aerosp. Electron. Syst. 48(1):159–169, 2012), which we refer to as Eigen-value decomposition and Received Signal strength Indicator-based method (Eigen-RSSI), was able to estimate 3-D location parameters of a single source efficiently. However, it can only be applied to an extended AVS which consists of a pressure sensor separated from the velocity sensors by a certain distance. In this paper, we propose a uni-AVS MUSIC (U-MUSIC) approach for 3-D location parameter estimation based on a compact AVS structure. We decouple the 3-D localization problem into step-by-step estimation of azimuth, elevation, and range and derive closed-form solutions for these parameter estimates by which a complex 3-D search for the parameters can be avoided. We show that the proposed approach outperforms the existing Eigen-RSSI method when the sensor system is required to be mounted in a confined space.