Adel Mohammadpour | AmirKabir University Of Technology (original) (raw)
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Papers by Adel Mohammadpour
Statistics & Probability Letters, 2004
Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method t... more Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method together with an S-PLUS function for simulating such a vector are introduced. Simulated values are used to plot contours of their empirical density.
Computational Statistics, 2000
ABSTRACT This works concerns the simulation of an exchangeable stable random vector. A characteri... more ABSTRACT This works concerns the simulation of an exchangeable stable random vector. A characterization for exchangeability of a stable random vector, in terms of its spectral measure, is given. The Modarres and Nolan's simulating method on stable random vectors is modified to the exchangeable case. FORTRAN subroutines to simulate a desirable exchangeable stable random vector and to create an exchangeable partition are written.
Statistics & Probability Letters, 2004
Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method t... more Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method together with an S-PLUS function for simulating such a vector are introduced. Simulated values are used to plot contours of their empirical density.
The problem of hypothesis testing with a nuisance parameter is considered. Two methods for using ... more The problem of hypothesis testing with a nuisance parameter is considered. Two methods for using fuzzy knowledge on the nuisance parameter to test hypotheses are suggested. These methods are neither a pure classical nor a pure Bayesian approach to hypothesis testing, but rather related to both. A few known examples and their applications, which cannot be studied by the parametric statistical methods, are discussed.
Consider an exchangeable normal vector with parameters µ, σ 2 , and ρ. On the basis of a vector o... more Consider an exchangeable normal vector with parameters µ, σ 2 , and ρ. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given. * 2 , where α = 0.05, µ 0 = 0, σ 0 2 = 1, µ = 0, σ 2 = 1, ρ = 0.5, and p = 10.
Our purpose in this paper is to provide an alternative approach to the Parametric Empirical Bayes... more Our purpose in this paper is to provide an alternative approach to the Parametric Empirical Bayes (PEB) approach to wavelet threshold selection. We propose an approach to wavelet threshold selection when we have a few prior candidates for the wavelet coefficients. In the other words, instead of PEB estimation of the threshold, we perform a prior selection and then estimate the threshold.
In this paper we introduce a method for prior selection. This method can be considered as an alte... more In this paper we introduce a method for prior selection. This method can be considered as an alternative approach to the parametric or nonparametric empirical Bayes method for prior selection.
Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussi... more Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussian stable random variables play the role of normal distribution in the central limit theorem, for normalized sums of random variables with infinite variance. The lack of analytic formula for density and distribution functions of stable random variables has been a major drawback to the use of stable distributions, also in the case of inference in Bayesian framework. Buckle introduced priors for the parameters of stable random variables to obtain an analytic form of posterior distribution. However, many researchers tried to solve the problem, through the Markov chain Monte Carlo methods, e.g. [8] and their references. In this paper a new class of heavy-tailed distribution is introduced, called skewed stable. This class has two main advantages: It has many inferential advantages, since it is a member of exponential family, so the Bayesian inference can be drawn similar to the exponential family of distributions and modelling skew data with stable distributions is dominated by this family. Finally, Bayesian inference for skewed stable arc compared to the stable distributions through a few simulations study.
Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statis... more Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statistical inference of mixture models [3, 4]. By noting the advantages of the Bayesian methods, practitioners prefer them. However, implementing Markov chain Monte Carlo algorithms can be very complicated for stable distributions, due to the non-analytic density or distribution function formulas.In this paper, we introduce a new class of mixture of heavy-tailed distributions, called mixture of skewed stable distributions. Skewed stable distributions belongs to the exponential family and they have analytic density representation. It is shown that skewed stable distributions dominate skew stable distribution functions and they can be used to model heavy-tailed data.The class of skewed stable distributions has an analytic representation for its density function and the Bayesian inference can be done similar to the exponential family of distributions.Finally, mixture of skewed stable distributions are compared to the mixture of stable distributions through a simulations study.
The family of skew distributions introduced by Azzalini and extended by others has received wides... more The family of skew distributions introduced by Azzalini and extended by others has received widespread attention. However, it suffers from complicated inference procedures. In this paper, a new family of skew distributions that overcomes the difficulties is introduced. This new family belongs to the exponential family. Many properties of this family are studied, inference procedures developed and simulation studies performed to assess the procedures. Some particular cases of this family, evidence of its flexibility and a real data application are presented. At least ten advantages of the new family over Azzalini's distributions are established.
Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statis... more Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statistical inference of mixture models [3, 4]. By noting the advantages of the Bayesian methods, practitioners prefer them. However, implementing Markov chain Monte Carlo algorithms can be very complicated for stable distributions, due to the non-analytic density or distribution function formulas. In this paper, we introduce a new class of mixture of heavy-tailed distributions, called mixture of skewed stable distributions. Skewed stable distributions belongs to the exponential family and they have analytic density representation. It is shown that skewed stable distributions dominate skew stable distribution functions and they can be used to model heavy-tailed data. The class of skewed stable distributions has an analytic representation for its density function and the Bayesian inference can be done similar to the exponential family of distributions. Finally, mixture of skewed stable distributions are compared to the mixture of stable distributions through a simulations study.
Statistics & Probability Letters, 2004
Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method t... more Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method together with an S-PLUS function for simulating such a vector are introduced. Simulated values are used to plot contours of their empirical density.
Computational Statistics, 2000
ABSTRACT This works concerns the simulation of an exchangeable stable random vector. A characteri... more ABSTRACT This works concerns the simulation of an exchangeable stable random vector. A characterization for exchangeability of a stable random vector, in terms of its spectral measure, is given. The Modarres and Nolan's simulating method on stable random vectors is modified to the exchangeable case. FORTRAN subroutines to simulate a desirable exchangeable stable random vector and to create an exchangeable partition are written.
Statistics & Probability Letters, 2004
Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method t... more Certain characterizations for an exchangeable sub-Gaussian random vector are given and a method together with an S-PLUS function for simulating such a vector are introduced. Simulated values are used to plot contours of their empirical density.
The problem of hypothesis testing with a nuisance parameter is considered. Two methods for using ... more The problem of hypothesis testing with a nuisance parameter is considered. Two methods for using fuzzy knowledge on the nuisance parameter to test hypotheses are suggested. These methods are neither a pure classical nor a pure Bayesian approach to hypothesis testing, but rather related to both. A few known examples and their applications, which cannot be studied by the parametric statistical methods, are discussed.
Consider an exchangeable normal vector with parameters µ, σ 2 , and ρ. On the basis of a vector o... more Consider an exchangeable normal vector with parameters µ, σ 2 , and ρ. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given. * 2 , where α = 0.05, µ 0 = 0, σ 0 2 = 1, µ = 0, σ 2 = 1, ρ = 0.5, and p = 10.
Our purpose in this paper is to provide an alternative approach to the Parametric Empirical Bayes... more Our purpose in this paper is to provide an alternative approach to the Parametric Empirical Bayes (PEB) approach to wavelet threshold selection. We propose an approach to wavelet threshold selection when we have a few prior candidates for the wavelet coefficients. In the other words, instead of PEB estimation of the threshold, we perform a prior selection and then estimate the threshold.
In this paper we introduce a method for prior selection. This method can be considered as an alte... more In this paper we introduce a method for prior selection. This method can be considered as an alternative approach to the parametric or nonparametric empirical Bayes method for prior selection.
Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussi... more Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussian stable random variables play the role of normal distribution in the central limit theorem, for normalized sums of random variables with infinite variance. The lack of analytic formula for density and distribution functions of stable random variables has been a major drawback to the use of stable distributions, also in the case of inference in Bayesian framework. Buckle introduced priors for the parameters of stable random variables to obtain an analytic form of posterior distribution. However, many researchers tried to solve the problem, through the Markov chain Monte Carlo methods, e.g. [8] and their references. In this paper a new class of heavy-tailed distribution is introduced, called skewed stable. This class has two main advantages: It has many inferential advantages, since it is a member of exponential family, so the Bayesian inference can be drawn similar to the exponential family of distributions and modelling skew data with stable distributions is dominated by this family. Finally, Bayesian inference for skewed stable arc compared to the stable distributions through a few simulations study.
Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statis... more Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statistical inference of mixture models [3, 4]. By noting the advantages of the Bayesian methods, practitioners prefer them. However, implementing Markov chain Monte Carlo algorithms can be very complicated for stable distributions, due to the non-analytic density or distribution function formulas.In this paper, we introduce a new class of mixture of heavy-tailed distributions, called mixture of skewed stable distributions. Skewed stable distributions belongs to the exponential family and they have analytic density representation. It is shown that skewed stable distributions dominate skew stable distribution functions and they can be used to model heavy-tailed data.The class of skewed stable distributions has an analytic representation for its density function and the Bayesian inference can be done similar to the exponential family of distributions.Finally, mixture of skewed stable distributions are compared to the mixture of stable distributions through a simulations study.
The family of skew distributions introduced by Azzalini and extended by others has received wides... more The family of skew distributions introduced by Azzalini and extended by others has received widespread attention. However, it suffers from complicated inference procedures. In this paper, a new family of skew distributions that overcomes the difficulties is introduced. This new family belongs to the exponential family. Many properties of this family are studied, inference procedures developed and simulation studies performed to assess the procedures. Some particular cases of this family, evidence of its flexibility and a real data application are presented. At least ten advantages of the new family over Azzalini's distributions are established.
Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statis... more Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statistical inference of mixture models [3, 4]. By noting the advantages of the Bayesian methods, practitioners prefer them. However, implementing Markov chain Monte Carlo algorithms can be very complicated for stable distributions, due to the non-analytic density or distribution function formulas. In this paper, we introduce a new class of mixture of heavy-tailed distributions, called mixture of skewed stable distributions. Skewed stable distributions belongs to the exponential family and they have analytic density representation. It is shown that skewed stable distributions dominate skew stable distribution functions and they can be used to model heavy-tailed data. The class of skewed stable distributions has an analytic representation for its density function and the Bayesian inference can be done similar to the exponential family of distributions. Finally, mixture of skewed stable distributions are compared to the mixture of stable distributions through a simulations study.