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Journal articles on the topic 'And shrinkage estimator (SE)'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Zakerzadeh, Hojatollah, Ali Akbar Jafari, and Mahdieh Karimi. "Optimal Shrinkage Estimations for the Parameters of Exponential Distribution Based on Record Values." Revista Colombiana de Estadística 39, no. 1 (January 18, 2016): 33–44. http://dx.doi.org/10.15446/rce.v39n1.55137.

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<p>This paper studies shrinkage estimation after the preliminary test for the parameters of exponential distribution based on record values. The optimal value of shrinkage coefficients is also obtained based on the minimax regret criterion. The maximum likelihood, pre-test, and shrinkage estimators are compared using a simulation study. The results to estimate the scale parameter show that the optimal shrinkage estimator is better than the maximum likelihood estimator in all cases, and when the prior guess is near the true value, the pre-test estimator is better than shrinkage estimator. The results to estimate the location parameter show that the optimal shrinkage estimator is better than maximum likelihood estimator when a prior guess is close<br />to the true value. All estimators are illustrated by a numerical example.</p>

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2

Saleh, A. K. Md Ehsanes, M. Arashi, M. Norouzirad, and B. M. Goalm Kibria. "On shrinkage and selection: ANOVA model." Journal of Statistical Research 51, no. 2 (February 1, 2018): 165–91. http://dx.doi.org/10.47302/jsr.2017510205.

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This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estimator (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We compare and contrast the L2-risk of all the estimators with the lower bound of L2-risk of LASSO in a family of diagonal projection scheme which is also the lower bound of the exact L2-risk of LASSO. The result of this comparison is that neither LASSO nor the LSE, preliminary test, and Stein-type estimators outperform each other uniformly. However, when the model is sparse, LASSO outperforms all estimators except “ridge” estimator since both LASSO and ridge are L2-risk equivalent under sparsity. We also find that LASSO and the restricted LSE are L2-risk equivalent and both outperform all estimators (except ridge) depending on the dimension of sparsity. Finally, ridge estimator outperforms all estimators uniformly. Our finding are based on L2-risk of estimators and lower bound of the risk of LASSO together with tables of efficiency and graphical display of efficiency and not based on simulation.

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3

Hansen, Bruce E. "SHRINKAGE EFFICIENCY BOUNDS." Econometric Theory 31, no. 4 (October 2, 2014): 860–79. http://dx.doi.org/10.1017/s0266466614000693.

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This paper is an extension of Magnus (2002, Econometrics Journal 5, 225–236) to multiple dimensions. We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the efficiency bound (the lowest achievable risk) for minimax shrinkage estimation in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976, Annals of Statistics 4, 11–21). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.

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Afshari, Mahmoud, and Hamid Karamikabir. "The Location Parameter Estimation of Spherically Distributions with Known Covariance Matrices." Statistics, Optimization & Information Computing 8, no. 2 (February 20, 2020): 499–506. http://dx.doi.org/10.19139/soic-2310-5070-710.

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This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known.We compared the present estimator with natural estimator by using risk function.We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.

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5

Prakash, Gyan. "Some Estimators for the Pareto Distribution." Journal of Scientific Research 1, no. 2 (April 22, 2009): 236–47. http://dx.doi.org/10.3329/jsr.v1i2.1642.

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We derive some shrinkage test-estimators and the Bayes estimators for the shape parameter of a Pareto distribution under the general entropy loss (GEL) function. The properties have been studied in terms of relative efficiency. The choices of shrinkage factor are also suggested. Â Keywords: General entropy loss; Shrinkage factor; Shrinkage test-estimator; Bayes estimator; Relative efficiency.Â Â© 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.Â DOI: 10.3329/jsr.v1i2.1642Â Â

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6

Kambo, N. S., B. R. Fanda, and Z. A. Al-Hemyari. "On huntseerger type shrinkage estimator." Communications in Statistics - Theory and Methods 21, no. 3 (January 1992): 823–41. http://dx.doi.org/10.1080/03610929208830817.

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7

Hassan, N. J., J. Mahdi Hadad, and A. Hawad Nasar. "Bayesian Shrinkage Estimator of Burr XII Distribution." International Journal of Mathematics and Mathematical Sciences 2020 (June 22, 2020): 1–6. http://dx.doi.org/10.1155/2020/7953098.

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In this paper, we derive the generalized Bayesian shrinkage estimator of parameter of Burr XII distribution under three loss functions: squared error, LINEX, and weighted balance loss functions. Therefore, we obtain three generalized Bayesian shrinkage estimators (GBSEs). In this approach, we find the posterior risk function (PRF) of the generalized Bayesian shrinkage estimator (GBSE) with respect to each loss function. The constant formula of GBSE is computed by minimizing the PRF. In special cases, we derive two new GBSEs under the weighted loss function. Finally, we give our conclusion.

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8

OKHRIN, YAREMA, and WOLFGANG SCHMID. "ESTIMATION OF OPTIMAL PORTFOLIO WEIGHTS." International Journal of Theoretical and Applied Finance 11, no. 03 (May 2008): 249–76. http://dx.doi.org/10.1142/s0219024908004798.

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The paper discusses finite sample properties of optimal portfolio weights, estimated expected portfolio return, and portfolio variance. The first estimator assumes the asset returns to be independent, while the second takes them to be predictable using a linear regression model. The third and the fourth approaches are based on a shrinkage technique and a Bayesian methodology, respectively. In the first two cases, we establish the moments of the weights and the portfolio returns. A consistent estimator of the shrinkage parameter for the third estimator is then derived. The advantages of the shrinkage approach are assessed in an empirical study.

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9

Carriero, Andrea, George Kapetanios, and Massilimiano Marcellino. "A Shrinkage Instrumental Variable Estimator for Large Datasets." Articles 91, no. 1-2 (May 20, 2016): 67–87. http://dx.doi.org/10.7202/1036914ar.

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This paper proposes and discusses an instrumental variable estimator that can be of particular relevance when many instruments are available and/or the number of instruments is large relative to the total number of observations. Intuition and recent work (see, e.g., Hahn, 2002) suggest that parsimonious devices used in the construction of the final instruments may provide effective estimation strategies. Shrinkage is a well known approach that promotes parsimony. We consider a new shrinkage 2SLS estimator. We derive a consistency result for this estimator under general conditions, and via Monte Carlo simulation show that this estimator has good potential for inference in small samples.

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10

Al-Zahrani, Bander. "On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study." International Journal of Statistics and Probability 5, no. 4 (June 11, 2016): 1. http://dx.doi.org/10.5539/ijsp.v5n4p1.

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The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

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11

Xiao, Hui, and Yiguo Sun. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study." Journal of Risk and Financial Management 12, no. 3 (June 26, 2019): 109. http://dx.doi.org/10.3390/jrfm12030109.

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Model selection and model averaging are popular approaches for handling modeling uncertainties. The existing literature offers a unified framework for variable selection via penalized likelihood and the tuning parameter selection is vital for consistent selection and optimal estimation. Few studies have explored the finite sample performances of the class of ordinary least squares (OLS) post-selection estimators with the tuning parameter determined by different selection approaches. We aim to supplement the literature by studying the class of OLS post-selection estimators. Inspired by the shrinkage averaging estimator (SAE) and the Mallows model averaging (MMA) estimator, we further propose a shrinkage MMA (SMMA) estimator for averaging high-dimensional sparse models. Our Monte Carlo design features an expanding sparse parameter space and further considers the effect of the effective sample size and the degree of model sparsity on the finite sample performances of estimators. We find that the OLS post-smoothly clipped absolute deviation (SCAD) estimator with the tuning parameter selected by the Bayesian information criterion (BIC) in finite sample outperforms most penalized estimators and that the SMMA performs better when averaging high-dimensional sparse models.

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12

Omer, Talha, Zawar Hussain, Muhammad Qasim, Said Farooq Shah, and Akbar Ali Khan. "Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution." Journal of Modern Applied Statistical Methods 19, no. 1 (June 8, 2021): 2–21. http://dx.doi.org/10.22237/jmasm/1608553440.

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Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

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13

Abdulkareem Abdulazeez, Qamar, and Zakariya Yahya Algamal. "Employing particle swarm optimization algorithm for shrinkage parameter estimation in generalized Liu estimator." International Journal of Advanced Statistics and Probability 8, no. 1 (May 15, 2020): 10. http://dx.doi.org/10.14419/ijasp.v8i1.30565.

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It is well-known that in the presence of multicollinearity, the Liu estimator is an alternative to the ordinary least square (OLS) estimator and the ridge estimator. Generalized Liu estimator (GLE) is a generalization of the Liu estimator. However, the efficiency of GLE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GLE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performance of the proposed method in terms of prediction error.

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14

Xiao, Min, Ting Chen, Kunpeng Huang, and Ruixing Ming. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing." Journal of Systems Science and Information 8, no. 6 (December 1, 2020): 549–64. http://dx.doi.org/10.21078/jssi-2020-549-16.

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Abstract Detecting differential expression of genes in genom research (e.g., 2019-nCoV) is not uncommon, due to the cost only small sample is employed to estimate a large number of variances (or their inverse) of variables simultaneously. However, the commonly used approaches perform unreliable. Borrowing information across different variables or priori information of variables, shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic. In this paper, we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution. Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well. In addition, application comparison and real data analysis indicate that the proposed estimator also works well.

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15

Botts, Carsten H., and Michael J. Daniels. "A shrinkage estimator for spectral densities." Biometrika 93, no. 1 (March 1, 2006): 179–95. http://dx.doi.org/10.1093/biomet/93.1.179.

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16

George, Edward I. "A formal bayes multiple shrinkage estimator." Communications in Statistics - Theory and Methods 15, no. 7 (January 1986): 2099–114. http://dx.doi.org/10.1080/03610928608829237.

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17

Sun, Chenwei, Haihong Tao, Jiaqi Song, and Langxu Zhao. "Mainlobe maintenance using shrinkage estimator method." IET Signal Processing 12, no. 2 (April 2018): 169–73. http://dx.doi.org/10.1049/iet-spr.2016.0691.

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18

Park, Junyong. "Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators." Statistics & Probability Letters 93 (October 2014): 1–6. http://dx.doi.org/10.1016/j.spl.2014.06.005.

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19

Raheem, Sairan Hamza, Bayda Atiya Kalaf, and Abbas Najim Salman. "Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)." Baghdad Science Journal 18, no. 2(Suppl.) (June 20, 2021): 1103. http://dx.doi.org/10.21123/bsj.2021.18.2(suppl.).1103.

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In this study, the stress-strength model R = P(Y < X < Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.

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20

De Gregorio, Alessandro, and Stefano M. Iacus. "ADAPTIVE LASSO-TYPE ESTIMATION FOR MULTIVARIATE DIFFUSION PROCESSES." Econometric Theory 28, no. 4 (February 21, 2012): 838–60. http://dx.doi.org/10.1017/s0266466611000806.

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The least absolute shrinkage and selection operator (LASSO) is a widely used statistical methodology for simultaneous estimation and variable selection. It is a shrinkage estimation method that allows one to select parsimonious models. In other words, this method estimates the redundant parameters as zero in the large samples and reduces variance of estimates. In recent years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive LASSO problem for discretely observed multivariate diffusion processes. We prove oracle properties and also derive the asymptotic distribution of the LASSO estimator. This is a nontrivial extension of previous results by Wang and Leng (2007, Journal of the American Statistical Association, 102(479), 1039–1048) on LASSO estimation because of different rates of convergence of the estimators in the drift and diffusion coefficients. We perform simulations and real data analysis to provide some evidence on the applicability of this method.

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21

Månsson, Kristofer, B. M. Golam Kibria, and Ghazi Shukur. "A New Liu Type of Estimator for the Restricted SUR Estimator." Journal of Modern Applied Statistical Methods 18, no. 1 (March 25, 2020): 2–11. http://dx.doi.org/10.22237/jmasm/1556669340.

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A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.

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22

Zhang, Bin. "Improved Shrinkage Estimator of Large-Dimensional Covariance Matrix under the Complex Gaussian Distribution." Mathematical Problems in Engineering 2020 (July 7, 2020): 1–8. http://dx.doi.org/10.1155/2020/6527462.

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Estimating the covariance matrix of a random vector is essential and challenging in large dimension and small sample size scenarios. The purpose of this paper is to produce an outperformed large-dimensional covariance matrix estimator in the complex domain via the linear shrinkage regularization. Firstly, we develop a necessary moment property of the complex Wishart distribution. Secondly, by minimizing the mean squared error between the real covariance matrix and its shrinkage estimator, we obtain the optimal shrinkage intensity in a closed form for the spherical target matrix under the complex Gaussian distribution. Thirdly, we propose a newly available shrinkage estimator by unbiasedly estimating the unknown scalars involved in the optimal shrinkage intensity. Both the numerical simulations and an example application to array signal processing reveal that the proposed covariance matrix estimator performs well in large dimension and small sample size scenarios.

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23

Karamikabir, Hamid, and Mahmoud Afshari. "Wavelet shrinkage generalized Bayes estimation for elliptical distribution parameter’s under LINEX loss." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 03 (May 2019): 1950009. http://dx.doi.org/10.1142/s0219691319500097.

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In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

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24

Fan, Qingliang, and Wei Zhong. "Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective." Journal of Business & Economic Statistics 36, no. 3 (April 28, 2017): 388–99. http://dx.doi.org/10.1080/07350015.2016.1180991.

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25

Salman, Abbas Najim, and Rana Hadi. "Preliminary test shrinkage estimators for the shape parameter of generalized exponential distribution." International Journal of Applied Mathematical Research 5, no. 4 (September 19, 2016): 162. http://dx.doi.org/10.14419/ijamr.v5i4.6573.

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The present paper deals with the estimation of the shape parameter α of Generalized Exponential GE (α, λ) distribution when the scale parameter λ is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.Comparisons between the proposed estimator withe classical estimator as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.

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26

Hamdaoui, Abdenour, Abdelkader Benkhaled, and Nadia Mezouar. "Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case." Statistics, Optimization & Information Computing 8, no. 2 (February 17, 2020): 507–20. http://dx.doi.org/10.19139/soic-2310-5070-735.

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In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested instudying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

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27

Jiewu Huang. "An Alternative Shrinkage Estimator in Linear Model." International Journal of Advancements in Computing Technology 5, no. 7 (April 15, 2013): 891–98. http://dx.doi.org/10.4156/ijact.vol5.issue7.110.

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28

Xiong, Jian, D. G. Chen, and Zhen-hai Yang. "A Shrinkage Estimator for Combination of Bioassays." Acta Mathematicae Applicatae Sinica, English Series 23, no. 3 (July 2007): 467–76. http://dx.doi.org/10.1007/s10255-007-0386-z.

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29

Khalil, Amoon, and Mohiedin Wainakh. "Enhanced Spectrum Sensing Algorithm Based on MME Detection and OAS Shrinkage Estimator." International Journal of Embedded and Real-Time Communication Systems 10, no. 1 (January 2019): 83–97. http://dx.doi.org/10.4018/ijertcs.2019010105.

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Spectrum Sensing is one of the major steps in Cognitive Radio. There are many methods to conduct Spectrum Sensing. Each method has different detection performances. In this article, the authors propose a modification of one of these methods based on MME algorithm and OAS estimator. In MME&OAS method, in each detection window, OAS estimates the covariance matrix of the signal then the MME algorithm detects the signal on the estimated matrix. In the proposed algorithm, authors assumed that there is correlation between two consecutive decisions, so authors suggest the OAS estimator depending on the last detection decision, and then detect the signal using MME algorithm. Simulation results showed enhancement in detection performance (about 2dB when detection probability is 0.9. compared to MME&OAS method).

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Sanchis, Charlotte, and Alfred Hanssen. "Sparse code shrinkage for signal enhancement of seismic data." GEOPHYSICS 76, no. 6 (November 2011): V151—V167. http://dx.doi.org/10.1190/geo2010-0128.1.

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Sparse code shrinkage is a method that is commonly used for image denoising and that has recently found some applications in seismic for random noise attenuation and multiple removal in a simplified form. Sparse coding finds a representation of the data in which each component is only rarely significantly active. Such a representation is closely related to independent component analysis. We discuss the link between sparse coding and independent component analysis, and show how the application of shrinkages to sparse components manages to attenuate the noise in seismic data. The use of data-driven shrinkages estimated from noise-free data is a necessary condition for this method to be efficient. We propose a realization of the data, attenuated in noise, that allows the derivation of data-driven shrinkage functions. They are obtained either by fitting this sparse representation with a given density model, or by estimating the density directly from the data. Two parametric models of density are investigated, the sparse density and the normal inverse Gaussian density, while the Gaussian kernel estimator estimates the density from the data. They are tested on both synthetic and real marine seismic data, and compared with f-x deconvolution and local SVD as alternative denoising methods. We show that the NIG density yields the best results, but the sparse density and the nonparametric density estimate are acceptable choices as well. Finally, the comparison with alternative methods shows that sparse code shrinkage is a credible alternative for the denoising of seismic data.

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COSTA, Luzia Aparecida, Lucas Monteiro CHAVES, and Devanil Jaques SOUZA. "PROPOSAL OF A RAO RIDGE TYPE ESTIMATOR." REVISTA BRASILEIRA DE BIOMETRIA 36, no. 3 (September 26, 2018): 286. http://dx.doi.org/10.28951/rbb.v36i3.283.

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Based on a geometrical interpretation of Ridge estimators a new Rao Ridge type estimator is proposed. Its advantage is to reach the optimum value for the shrinkage parameter more quickly. The geometry, the predictive capacity, a computational example, an application to real data and comparison with the usual Ridge estimator are developed.

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Fan, Qingliang, Xiao Han, Guangming Pan, and Bibo Jiang. "LARGE SYSTEM OF SEEMINGLY UNRELATED REGRESSIONS: A PENALIZED QUASI-MAXIMUM LIKELIHOOD ESTIMATION PERSPECTIVE." Econometric Theory 36, no. 3 (May 27, 2019): 526–58. http://dx.doi.org/10.1017/s026646661900015x.

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In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate of the estimated covariance matrix in terms of the Frobenius norm. The model selection consistency of the covariance matrix estimator is also established. Simulation results show that when the number of equations is large relative to the sample size and the error covariance matrix is sparse, the PQMLE outperforms other contemporary estimators.

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Angus, John E. "The Improved Estimation of σ in Quality Control, Revisited." Probability in the Engineering and Informational Sciences 11, no. 1 (January 1997): 37–42. http://dx.doi.org/10.1017/s0269964800004654.

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Recently, Derman and Ross (1995, An improved estimator of a in quality control, Probability in the Engineering and Informational Sciences 9: 411–415) derived an estimator of the standard deviation in the standard quality control model and showed that it had smaller mean squared error than the usual estimator. The new estimator was also shown to be consistent even when the underlying distribution deviates from normality, unlike the usual estimator. In this note, the mean squared error is further improved via shrinkage of the Derman-Ross estimator, and a consistent minimum variance unbiased estimator is presented. Finally, by making use of additional subgroup statistics, a minimum variance unbiased estimator is derived and further improved via shrinkage.

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Awondo, Sebastain N., Octavio A. Ramirez, Gauri S. Datta, Gregory Colson, and Esendugue G. Fonsah. "Estimation of Crop Yields and Insurance Premiums Using a Shrinkage Estimator." North American Actuarial Journal 22, no. 2 (April 3, 2018): 289–308. http://dx.doi.org/10.1080/10920277.2017.1404477.

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35

Dey, Sanku, Tanujit Dey, and Sudhansu S. Maiti. "Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data." Austrian Journal of Statistics 44, no. 4 (December 6, 2015): 3–15. http://dx.doi.org/10.17713/ajs.v44i4.71.

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This paper derives Bayes shrinkage estimator of Rayleigh parameter and its associated risk based on conjugate prior under the assumption of general entropy loss function for progressive type-II censored data. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. A procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the Rayleigh distribution fits a real data set.

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Abdulateef, Eman Ahmed, and Abbas Najim Salman. "On Shrinkage Estimation for R(s, k) in Case of Exponentiated Pareto Distribution." Ibn AL- Haitham Journal For Pure and Applied Science 32, no. 1 (February 10, 2019): 152. http://dx.doi.org/10.30526/32.1.1825.

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This paper concerns with deriving and estimating the reliability of the multicomponent system in stress-strength model R(s,k), when the stress and strength are identical independent distribution (iid), follows two parameters Exponentiated Pareto Distribution(EPD) with the unknown shape and known scale parameters. Shrinkage estimation method including Maximum likelihood estimator (MLE), has been considered. Comparisons among the proposed estimators were made depending on simulation based on mean squared error (MSE) criteria.

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Afshari, Mahmoud. "Nonlinear wavelet shrinkage estimator of nonparametric regularity regression function via cross-validation with simulation study." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 06 (November 2017): 1750057. http://dx.doi.org/10.1142/s0219691317500576.

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Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using [Formula: see text] software to compare purpose estimator with another estimators.

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38

Bodnar, Taras, Ostap Okhrin, and Nestor Parolya. "Optimal shrinkage estimator for high-dimensional mean vector." Journal of Multivariate Analysis 170 (March 2019): 63–79. http://dx.doi.org/10.1016/j.jmva.2018.07.004.

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Wen, Chao-Kai, Jung-Chieh Chen, and Pangan Ting. "A Shrinkage Linear Minimum Mean Square Error Estimator." IEEE Signal Processing Letters 20, no. 12 (December 2013): 1179–82. http://dx.doi.org/10.1109/lsp.2013.2283725.

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40

Hoque, Zahirul, Jacek Wesolowski, and Shahadut Hossain. "Shrinkage estimator of regression model under asymmetric loss." Communications in Statistics - Theory and Methods 47, no. 22 (November 27, 2017): 5547–57. http://dx.doi.org/10.1080/03610926.2017.1397169.

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41

Riley, Steven, and J. J. McDowell. "The WIG (weighted individual and group) shrinkage estimator." Journal of the Experimental Analysis of Behavior 111, no. 2 (February 1, 2019): 166–82. http://dx.doi.org/10.1002/jeab.503.

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42

LIU, YAN, NGAI HANG CHAN, CHI TIM NG, and SAMUEL PO SHING WONG. "SHRINKAGE ESTIMATION OF MEAN-VARIANCE PORTFOLIO." International Journal of Theoretical and Applied Finance 19, no. 01 (February 2016): 1650003. http://dx.doi.org/10.1142/s0219024916500035.

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This paper studies the optimal expected gain/loss of a portfolio at a given risk level when the initial investment is zero and the number of stocks [Formula: see text] grows with the sample size [Formula: see text]. A new estimator of the optimal expected gain/loss of such a portfolio is proposed after examining the behavior of the sample mean vector and the sample covariance matrix based on conditional expectations. It is found that the effect of the sample mean vector is additive and the effect of the sample covariance matrix is multiplicative, both of which over-predict the optimal expected gain/loss. By virtue of a shrinkage method, a new estimate is proposed when the sample covariance matrix is not invertible. The superiority of the proposed estimator is demonstrated by matrix inequalities and simulation studies.

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Salman, Abbas Najim, and Maymona Ameen. "On double stage minimax-shrinkage estimator for generalized Rayleigh model." International Journal of Applied Mathematical Research 5, no. 1 (February 10, 2016): 39. http://dx.doi.org/10.14419/ijamr.v5i1.5553.

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<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

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44

Yüzbaşı, Bahadır, and S. Ejaz Ahmed. "Ridge Type Shrinkage Estimation of Seemingly Unrelated Regressions And Analytics of Economic and Financial Data from “Fragile Five” Countries." Journal of Risk and Financial Management 13, no. 6 (June 18, 2020): 131. http://dx.doi.org/10.3390/jrfm13060131.

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In this paper, we suggest improved estimation strategies based on preliminarily test and shrinkage principles in a seemingly unrelated regression model when explanatory variables are affected by multicollinearity. To that end, we split the vector regression coefficient of each equation into two parts: one includes the coefficient vector for the main effects, and the other is a vector for nuisance effects, which could be close to zero. Therefore, two competing models per equation of the system regression model are obtained: one includes all the regression of coefficients (full model); the other (sub model) includes only the coefficients of the main effects based on the auxiliary information. The preliminarily test estimation improves the estimation procedure if there is evidence that the vector of nuisance parameters does not provide a useful contribution to the model. The shrinkage estimation method shrinks the full model estimator in the direction of the sub-model estimator. We conduct a Monte Carlo simulation study in order to examine the relative performance of the suggested estimation strategies. More importantly, we apply our methodology based on the preliminarily test and the shrinkage estimations to analyse economic data by investigating the relationship between foreign direct investment and several economic variables in the “Fragile Five” countries between 1983 and 2018.

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45

Liao, Zhipeng. "ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION." Econometric Theory 29, no. 5 (February 25, 2013): 857–904. http://dx.doi.org/10.1017/s0266466612000783.

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This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

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Xiao, Hui, and Yiguo Sun. "Forecasting the Returns of Cryptocurrency: A Model Averaging Approach." Journal of Risk and Financial Management 13, no. 11 (November 13, 2020): 278. http://dx.doi.org/10.3390/jrfm13110278.

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This paper aims to enrich the understanding and modelling strategies for cryptocurrency markets by investigating major cryptocurrencies’ returns determinants and forecast their returns. To handle model uncertainty when modelling cryptocurrencies, we conduct model selection for an autoregressive distributed lag (ARDL) model using several popular penalized least squares estimators to explain the cryptocurrencies’ returns. We further introduce a novel model averaging approach or the shrinkage Mallows model averaging (SMMA) estimator for forecasting. First, we find that the returns for most cryptocurrencies are sensitive to volatilities from major financial markets. The returns are also prone to the changes in gold prices and the Forex market’s current and lagged information. Then, when forecasting cryptocurrencies’ returns, we further find that an ARDL(p,q) model estimated by the SMMA estimator outperforms the competing estimators and models out-of-sample.

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Kim, Kyong-Il, Soon-Ic Bahng, and Ryong-Nam Choe. "Despeckling method of ultrasound images using closed-form shrinkage function based on cauchy distribution in wavelet domain." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 04 (June 5, 2020): 2050026. http://dx.doi.org/10.1142/s0219691320500265.

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Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ([Formula: see text]) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.

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Boudt, Kris, Dries Cornilly, and Tim Verdonck. "A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables*." Journal of Financial Econometrics 18, no. 1 (October 4, 2018): 1–23. http://dx.doi.org/10.1093/jjfinec/nby022.

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Abstract Decision-making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical sample estimator of the coskewness matrix performs poorly for small sample sizes. A solution is to use shrinkage estimators, defined as the convex combination between the sample coskewness matrix and a target matrix. We propose unbiased consistent estimators for the MSE loss function and include the possibility of having multiple target matrices. In a portfolio application, we find that the proposed shrinkage coskewness estimators are useful in mean–variance–skewness efficient portfolio allocation of funds of hedge funds.

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49

Caner, Mehmet. "LASSO-TYPE GMM ESTIMATOR." Econometric Theory 25, no. 1 (February 2009): 270–90. http://dx.doi.org/10.1017/s0266466608090099.

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This paper proposes the least absolute shrinkage and selection operator–type (Lasso-type) generalized method of moments (GMM) estimator. This Lasso-type estimator is formed by the GMM objective function with the addition of a penalty term. The exponent of the penalty term in the regular Lasso estimator is equal to one. However, the exponent of the penalty term in the Lasso-type estimator is less than one in the analysis here. The magnitude of the exponent is reduced to avoid the asymptotic bias. This estimator selects the correct model and estimates it simultaneously. In other words, this method estimates the redundant parameters as zero in the large samples and provides the standard GMM limit distribution for the estimates of the nonzero parameters in the model. The asymptotic theory for our estimator is nonstandard. We conduct a simulation study that shows that the Lasso-type GMM correctly selects the true model much more often than the Bayesian information Criterion (BIC) and another model selection procedure based on the GMM objective function.

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50

Handa, B. R., Rajeev Kumar, and R. K. Tuteja. "A multiparameter extension of two stage modified shrinkage estimator." Communications in Statistics - Simulation and Computation 22, no. 2 (January 1993): 387–97. http://dx.doi.org/10.1080/03610919308813099.

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