ناتینگهام، ناتینگهام، انگلستان
دانشگاه شهید بهشتی، تهران، ایران
دانشگاه شهید چمران اهواز، اهواز، ایران
علاقه مندی موسی گلعلی زاده به آمار در دوره کارشناسی ارشد آمار وقتی که تحت راهنمایی دکتر سیامک نوربلوچی پایان نامه کارشناسی ارشدش را می نوشت شکل گرفت. بعد از وقفه ای حدودا پنج ساله و بعد از پذیرش در آزمون دوره دکتری اعزام به خارج به دانشگاه ناتینگهام انگلستان رفت. ایشان رساله اش را تحت راهنمایی پروفسور درایدن و پروفسور بال نوشت. در این دوره ایشان به شاخه جدیدی از آمار به نام آمارشکل وارد شد. او دوره پسادکتری در رگرسیون چندسطحی را با نظارت پروفسور براون در دانشگاه بریستول انجام داد. ایشان از سال 1387 فعالیت علمی خود را در گروه آمار دانشگاه تربیت مدرس شروع کرد و از آن تاریخ در هر دو گرایش ذکر شده به تحقیقاتش ادامه داد.
Sometimes, invoking a single causal relationship to explain dependency between variables might not be appropriate particularly in some economic problems. Instead, two jointly related equations, where one of the explanatory variables is endogenous, can represent the actual inheritance inter-relationship among variables. Such typical models are called simultaneous equation models of which the seemingly unrelated regression (SUR) models is a special case. Substantial progress has been made regarding the statistical inference on estimating the parameters of these models in which errors follow a normal distribution. But, less research was devoted to a case that the distributions of the errors are asymmetric. In this paper, statistical inference
The current article is a translation of a paper published in Significance journal, 2020, Vol. 17, No. 4 captioned as “CR Rao’s Centurychr (chr (chr ('39') 39chr ('39')) 39chr (chr ('39') 39chr ('39'))) chr (chr (chr ('39') 39chr ('39')) 39chr (chr ('39') 39chr ('39'))), which has been scripted as a perception of an appreciation note by involvements of Bradley Efron, Shun-ichi Amari, Donald B. Rubin, Arni SR Srinivasa Rao and David R. Cox. Therefore, it is not possible to address this manuscript as a scientific paper, which is regularly accepted among the researchers. Evidently, the proposed translated article is prepared with the focus on appreciating professor Rao’sa century contribution in statistics. With this intention, Persian sp
Multivariate circular observations, ie points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the log-likelihood function involves an infinite sum of indices in, where p is the dimension of the data. To overcome this problem, for moderate dimension p, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulat
One of the most common problems that any technique encounters is the high dimensionality of the input data. This yields several problems in the subsequently statistical methods due to so called" curse of dimensionality". Several dimension reduction methods have been proposed in the literature, until now, to accomplish the goal of having smaller dimension space. The most popular among them, is the so called Principal Component Analysis (PCA). One of the extensions of PCA is Probabilistic PCA (known as PPCA). In PPCA, a probabilistic model is used to perform the dimension reduction. By convention, there are cases in applied sciences, eg Bioinformatics, Biology and Geology that the data at hand are in non Euclidean space. Elaborating further,
In some fields, there is an interest in distinguishing different geometrical objects from each other. A field of research that studies the objects from a statistical point of view, provided they are invariant under translation, rotation and scaling effects, is known as the statistical shape analysis. Having some objects that are registered using key points on the outline of the objects, the main purpose of this paper is to compare two popular clustering procedures to cluster objects. We also use some indexes to evaluate our clustering application. The proposed methods are applied to the real life data.
The Pearson type family densities are among the most important classes of distributions that play a key role in the directional statistics. Their particular structures make them suitable candidates to analysis data on non-Euclidean space, such as sphere. To model data scattered asymmetrically on such spaces, the researchers confined themselves to extend particular distributions from the class of the Pearson type family densities. Those specific distributions are symmetric in nature but their extended versions are usually heavy tailed. In this paper, we introduce some alternative probability density functions in the class of Pearson type distributions on the sphere having the spherical Student’s , Fisher and Chi-square densities as the sub
One of the important problems in the statistical shape analysis context is to predict the shape change. Rather than taking the change in terms of time, we confine ourselves to the deformation of the objects represented by a regression-type model. We properly combine the shape definition in terms of the Kendall and Bookstein shape coordinate systems to break down the problem on the sphere. This is achieved through the triangulation of objects; a very popular technique in geometrical mathematics. A novel idea on tracing the residuals of the spherical regression is then proposed, enabling us to invoke the well-known spherical distributions, including von Mises–Fisher density, to make the statistical inference. New directional residuals not o
• The simultaneous equation models (SEMs) are one of the standard statistical tools for analyzing multivariate regression when the errors are correlated with some covariates. A particular version of the SEMs is the Seemingly Unrelated Regression (SUR) models which consist of several regression equations with errors being correlated across the equations. There are many occasions in which the normality assumption for the error term might not hold in these models. Although transforming the error to comply with the normal density is a solution, the interpretation of the estimators for the parameters and the associated model might not be straightforward. However, taking into account the skew-normal distribution for the error might, sometimes,
Recalling the definition of shape as a point on hyper-sphere, proposed by Kendall, the regression model is studied in this paper. In order to simplify the modeling, the triangulation via two landmarks is proposed. The triangulation not only simplifies the regression modelling of the shapes but also provides straightforward computation procedure to reconstruct geometrical structure of the objects. Novelty of the proposed method in this paper is on using the predictor variable, based upon the shape, which suitably describes the geometrical variability of the response. The comparison and evaluation of the proposed methods with the full Procrustes matching through the mean square error criteria are done. Application of two models for the config
Images, as the source of data, can be analyzed using some tools from spatial analysis. The key to do this task is Hidden Markov Random Field (HMRF). In this paper, we combine the HMRF with Latent Block Model (LBM) to both summarize large array of data sets in the images and to cluster the hyperspectral images. We show how spatial spectrum information can be invoked to shorten statistical inference on high dimensional images without confining to estimate a large numbers of parameters. This is provided by LBM framework on finding homogeneous blocks and then segmentation map among images. The outcome of such segmentation map is used in the spectral-spatial classification stage. To reduce data volume, a feature selection based on either Kullbac
The Principal Components Analysis is one of the popular exploratory approaches to reduce the dimension and to describe the main source of variation among data. Despite many benefits, it is encountered with some problems in multivariate analysis. Having outliers among data significantly influences the results of this method and it sounds a robust version of PCA is beneficial in this case. In addition, having moderate loadings in the final results makes the interpretation of principal components rather difficult. One can consider a version of sparse components in this case. We study a hybrid approach consisting of joint robust and sparse components and conduct some simulations to evaluate and compare it with other traditional methods. The pr
Some of the spherical distributions can be constructed through proper transformation of the densities on plane. Since the logistic density on the Euclidean space has similar behavior to the normal distribution, it is of interest to extend it for spherical data. In this paper, we introduce spherical logistic distribution on the unit sphere and then study relevant statistical inferences including parameters estimation through method of moments and maximum likelihood techniques. It is shown that the spherical logistic distribution is a multimodal distribution with the marginal logistic density function. Proposed density has rotational symmetry property and this plays a key role to drive some important results related to first two
One of the essential assumptions while working with the linear regression models based on the variation of the mean of response variables is independency among error components. To fail this assumption guide researchers to utilize linear mixed effect models. But, to use the latter models is dependent on absence of outliers, one can employ the linear mixed quantile models where error component follows asymmetric Laplace distribution. In this paper, the performance of the available frequentist estimation methods in these models was first evaluated through simulation studies. It is seen that the combined methods approximated quadrature Gauss and unsmooth optimization algorithm leads to more accurate estimators in compare with the stochastic ap
Multivariate circular observations, ie points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this model is quite complicated since each contribution in the log likelihood involve an infinite sum of indices in Z^ p where p is the dimension of the problem. To overcome this, two estimates procedures based on Expectation Maximization and Classification Expectation Maximization algorithms are proposed that worked well in moderate dimension size. The performance of the introduced methods are studied by Monte Carlo simulation and illustrated on three real data sets.
It is known that the shapes of planar triangles can be represented by a set of points on the surface of the unit sphere. On the other hand, most of the objects can easily be triangulated and so each triangle can accordingly be treated in the context of shape analysis. There is a growing interest to fit a smooth path going through the cloud of shape data available in some time instances. To tackle this problem, we propose a longitudinal model through a triangulation procedure for the shape data. In fact, our strategy initially relies on a spherical regression model for triangles, but is extended to shape data via triangulation. Regarding modeling of directional data, we use the bivariate von Mises–Fisher distribution for densi
رد طﺎﻘﻧ ﻦﯾا ﯽﺗرﺎﮐد تﺎﺼﺘﺨﻣ نداد راﺮﻗ و ءﺎﯿﺷا ﺢﻄﺳ یور ٢ﺺﺧﺎﺷ طﺎﻘﻧ یداﺪﻌﺗ سﺎﺳا ﺮﺑ (١ ﯽﺳﺪﻨﻫ ﻂﺳﻮﺗ ﺺﺧﺎﺷ ﻪﻄﻘﻧ L ﺎﺑ Rm یﺎﻀﻓ رد ﯽﺳﺪﻨﻫ یﺪﻨﺑﺮﮑﯿﭘ لﺎﺜﻣ ناﻮﻨﻋ ﻪﺑ. ﺖﺳا ٣ یﺪﻨﺑﺮﮑﯿﭘ ﺲﯾﺮﺗﺎﻣ قﺎﺒﻄﻧا (١٩٧٩) نارﺎﮑﻤﻫ و ﺎﯾدرﺎﻣ و (١٩٩٨) ﺎﯾدرﺎﻣ و نﺪﯾارد ﻪﺑ ﺎﻨﺑ. دﻮﺷ ﯽﻣ هداد ﺶﯾﺎﻤﻧ XL? m ﺲﯾﺮﺗﺎﻣ. دﺮﯿﮔ ﯽﻣ ترﻮﺻ (OPA) ۴ یدﺎﻋ ﺲﺘﺳاﺮﮐوﺮﭘ ﻞﯿﻠﺤﺗ ﻂﺳﻮﺗ Y و X ﯽﺷ ود راﺮﻗ یﺮﯿﮔ هزاﺪ
Background & Aim: The bootstrap is a method that resample from the original data set. There are the wide ranges of bootstrap application for estimating the prediction error rate. We compare some bootstrap methods for estimating prediction error in classification and choose the best method for the microarray leukemia classification.Methods & Materials: The sample consist of n= 38 patients with acute lymphoblastic leukemia (ALL) and acute myeloid leukemia (AML) with p= 4120 genes that n<< p from an existing database. We carried out following steps.(1) Resample from the original sample.(2) Divide the sample to two sets, learning set and test set by 3-fold cross validation.(3) Train 1NN, CART and DLDA classifiers and compute its misclassificati
Circular data are typical examples of directional data with a specific regular period. Because the presence of outliers leads to invalid statistical inferences on the parameters of the circular regression models, their prevalence in analyzing these models requires particular attentions. There are different approaches for modeling the structure of the data set with outliers in which using the mixture models is among the most important ones. As a new idea, to study the methods in determining the outlier data and to employ the mixture model of Von Mises distribution are considered in this paper. The EM algorithm is utilized to estimate the parameters of these models. The performance of the proposed models is investigated using some simulation
The instrumental variable (IV) regression is a common model in econometrics and other applied disciplines. This model is one of the proper candidate in dealing with endogeneity phenomenon which occurs in analyzing the multivariate regression when the errors are correlated with some covariates. One can consider IV regression as an special case of simultaneous equation models (SEM). There are some cases in which the normality assumption might not hold for the error term in these models and so the skew-normal distribution might be a suitable candidate. The present paper tackle the Bayesian inference based on Markov Chain Monte Carlo (MCMC) using this density for the error term while some instrumental variables are considered in the correspondi
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