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Showing 35 results for Estimator
Mehran Naghizadeh Qomi, Zohre Mahdizadeh, Hamid Zareefard,
Volume 12, Issue 1 (9-2018)
Abstract
Suppose that we have a random sample from one-parameter Rayleigh distribution. In classical methods, we estimate the interesting parameter based on the sample information and with usual estimators. Sometimes in practice, the researcher has some information about the unknown parameter in the form of a guess value. This guess is known as nonsample information. In this case, linear shrinkage estimators are introduced by combining nonsample and sample information which have smaller risk than usual estimators in the vicinity of guess and true value. In this paper, some shrinkage testimators are introduced using different methods based on vicinity of guess value and true parameter and their risks are computed under the entropy loss function. Then, the performance of shrinkage testimators and the best linear estimator is calculated via the relative efficiency of them. Therefore, the results are applied for the type-II censored data.
Mahdieh Mozafari, Mehrdad Naderi, Alireza Arabpour,
Volume 12, Issue 1 (9-2018)
Abstract
This paper introduces a new distribution based on extreme value distribution. Some properties and characteristics of the new distribution such as distribution function, moment generating function and skewness and kurtosis are studied. Finally, by computing the maximum likelihood estimators of the new distribution's parameters, the performance of the model is illustrated via two real examples.
Maryam Borzoei Bidgoli, Mohammad Arashi,
Volume 12, Issue 2 (3-2019)
Abstract
One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.
Mahdi Roozbeh, Morteza Amini,
Volume 13, Issue 2 (2-2020)
Abstract
In many fields such as econometrics, psychology, social sciences, medical sciences, engineering, etc., we face with multicollinearity among the explanatory variables and the existence of outliers in data. In such situations, the ordinary least-squares estimator leads to an inaccurate estimate. The robust methods are used to handle the outliers. Also, to overcome multicollinearity ridge estimators are suggested. On the other hand, when the error terms are heteroscedastic or correlated, the generalized least squares method is used. In this paper, a fast algorithm for computation of the feasible generalized least trimmed squares ridge estimator in a semiparametric regression model is proposed and then, the performance of the proposed estimators is examined through a Monte Carlo simulation study and a real data set.
Mahdi Teimouri,
Volume 14, Issue 1 (8-2020)
Abstract
The class of α-stable distributions incorporates both heavy tails and skewness and so are the most widely used class of distributions in several fields of study which incorporates both the skewness and heavy tails. Unfortunately, there is no closed-form expression for the density function of almost all of the members of this class, and so finding the maximum likelihood estimator for the parameters of this distribution is a challenging problem. In this paper, in order to tackle this issue, we propose some type of EM algorithm. The performance of the proposed EM algorithm is demonstrated via simulation and analyzing three sets of real data.
Mahmood Afshari, Abouzar Bazyari, Yeganeh Moradian, Hamid Karamikabir,
Volume 14, Issue 2 (2-2021)
Abstract
In this paper, the wavelet estimators of the nonparametric regression function based on the various thresholds under the mixture prior distribution and the mean square error loss function in Bosove space are computed. Also, using a simulation study the optimality of different wavelet thresholding estimators such as posterior mean, posterior median, Bayes factor, universal threshold and sure threshold are investigated. The results show that the average mean square error of sure threshold estimator is less than the other obtained estimators.
Mehran Naghizadeh Qomi,
Volume 14, Issue 2 (2-2021)
Abstract
In classical statistics, the parameter of interest is estimated based on sample information and using natural estimators such as maximum likelihood estimators. In Bayesian statistics, the Bayesian estimators are constructed based on prior knowledge and combining with it sample information. But, in some situations, the researcher has information about the unknown parameter as a guess. Bayesian shrinkage estimators can be constructed by Combining this non-sample information with sample information together with the prior knowledge, which is in the area of semi-classical statistics. In this paper, we introduce a class of Bayesian shrinkage estimators for the Weibull scale parameter as a generalization of the estimator at hand and consider the bias and risk of them under LINEX loss function. Then, the proposed estimators are compared using a real data set.
Mahdi Roozbeh, Monireh Maanavi,
Volume 14, Issue 2 (2-2021)
Abstract
The popular method to estimation the parameters of a linear regression model is the ordinary least square method which, despite the simplicity of calculating and providing the BLUE estimator of parameters, in some situations leads to misleading solutions. For example, we can mention the problems of multi-collinearity and outliers in the data set. The least trimmed squares method which is one of the most popular of robust regression methods decreases the influence of outliers as much as possible. The main goal of this paper is to provide a robust ridge estimation in order to model dental age data. Among the methods used to determine age, the most popular method throughout the world is the modern modified Demirjian method that is based on the calcification of the permanent tooth in panoramic radiography. It has been shown that using the robust ridge estimator is leading to reduce the mean squared error in comparison with the OLS method. Also, the proposed estimators were evaluated in simulated data sets.
Mozhgan Taavoni, Mohammad Arashi,
Volume 14, Issue 2 (2-2021)
Abstract
This paper considers the problem of simultaneous variable selection and estimation in a semiparametric mixed-effects model for longitudinal data with normal errors. We approximate the nonparametric function by regression spline and simultaneously estimate and select the variables under the optimization of the penalized objective function. Under some regularity conditions, the asymptotic behaviour of the resulting estimators is established in a high-dimensional framework where the number of parametric covariates increases as the sample size increases. For practical implementation, we use an EM algorithm to selects the significant variables and estimates the nonzero coefficient functions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed to illustrate the proposed procedure.
Eisa Mahmoudi, Soudabeh Sajjadipanah, Mohammad Sadegh Zamani,
Volume 16, Issue 1 (9-2022)
Abstract
In this paper, a modified two-stage procedure in the Autoregressive model AR(1) is considered, which investigates the point and the interval estimation of the mean based on the least-squares estimator. The modified two-stage procedure is as effective as the best fixed-sample size procedure. In this regard, the significant properties of the procedure, including asymptotic risk efficiency, first-order efficiency, consistent, and asymptotic distribution of the mean, are established. Then, a Monte Carlo simulation study is deduced to investigate the modified two-stage procedure. The performance of estimators and confidence intervals are evaluated utilizing a simulation study. Finally, real-time series data is considered to illustrate the applicability of the modified two-stage procedure.
Zahra Zandi, Hossein Bevrani,
Volume 16, Issue 2 (3-2023)
Abstract
This paper suggests Liu-type shrinkage estimators in linear regression model in the presence of multicollinearity under subspace information. The performance of the proposed estimators is compared to Liu-type estimator in terms of their relative efficiency via a Monte Carlo simulation study and a real data set. The results reveal that the proposed estimators outperform better than the Liu-type estimator.
Alla Alhamidah, Mehran Naghizadeh, ,
Volume 16, Issue 2 (3-2023)
Abstract
This paper discusses the Bayesian and E-Bayesian estimators in Burr type-XII model is discussed. The estimators are obtained based on type II censored data under the bounded reflected gamma loss function. The relationship between E-Bayesian estimators and their asymptotic properties is presented. The performance of the proposed estimators is evaluated using Monte Carlo simulation.
Dariush Najarzadeh,
Volume 17, Issue 1 (9-2023)
Abstract
In multiple regression analysis, the population multiple correlation coefficient (PMCC) is widely used to measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero PMCC based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data.
Fatemeh Ghapani, Babak Babadi,
Volume 17, Issue 2 (2-2024)
Abstract
In this paper, we introduce the weighted ridge estimators of fixed and random effects in stochastic restricted linear mixed measurement error models when collinearity is present. The asymptotic properties of the resulting estimates are examined. The necessary and sufficient conditions, for the superiority of the weighted ridge estimators against the weighted estimator in order to select the ridge parameter based on the mean squared error matrix of estimators, are investigated. Finally, theoretical results are augmented with a simulation study and a numerical example.
, Dr Seyed Kamran Ghoreishi,
Volume 18, Issue 1 (8-2024)
Abstract
In this paper, we first introduce semi-parametric heteroscedastic hierarchical models. Then, we define a new version of the empirical likelihood function (Restricted Joint Empirical likelihood) and use it to obtain the shrinkage estimators of the models' parameters in these models. Under different assumptions, a simulation study investigates the better performance of the restricted joint empirical likelihood function in the analysis of semi-parametric heterogeneity hierarchical models. Furthermore, we analyze an actual data set using the RJEL method.
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