Robert Mnatsakanov
West Virginia University, Statistics, Faculty Member
The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an... more
The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen-Weideman-Schmelzer and maximum entropy methods are presented via a simulation study.
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We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on... more
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping the cells and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two estimators is derived
Research Interests:
... Page 3. 254 Mnatsakanov and Hakobyan Note that our approach is particularly applicable in situations where other esti-mators cannot be used, eg, in situations where only moments (empirical) are avail-able. ... vO Page 5. 256... more
... Page 3. 254 Mnatsakanov and Hakobyan Note that our approach is particularly applicable in situations where other esti-mators cannot be used, eg, in situations where only moments (empirical) are avail-able. ... vO Page 5. 256 Mnatsakanov and Hakobyan ...
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The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences.... more
The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences. Uniform and L1-rates of convergence of moment-recovered pdfs are obtained. Finally, some applications and examples are briefly discussed.
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ABSTRACT The moment-recovered approximations of multivariate distributions are suggested. This method is natural in certain incomplete models where moments of the underlying distribution can be estimated from a sample of observed... more
ABSTRACT The moment-recovered approximations of multivariate distributions are suggested. This method is natural in certain incomplete models where moments of the underlying distribution can be estimated from a sample of observed distribution. This approach is applicable in situations where other methods cannot be used, e.g. in situations where only moments of the target distribution are available. Some properties of the proposed constructions are derived. In particular, procedures of recovering two types of convolutions, the copula and copula density functions, as well as the conditional density function, are suggested. Finally, the approximation of the inverse Laplace transform is obtained. The performance of moment-recovered construction is illustrated via graphs of a simple density function.
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We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on... more
We consider estimation of the structural distribution function of
the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping of the cells, and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two
estimators is derived by Poissonization and other, new, technical devices.
the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping of the cells, and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two
estimators is derived by Poissonization and other, new, technical devices.
Research Interests:
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on... more
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping the cells and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two estimators is derived by Poissonization and other, new, technical devices.
Research Interests:
This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and... more
This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and excess life distribution models are considered. The asymptotic normality and the rate of convergence in mean squared error (MSE) of the estimators are
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There are a large number of problems in imaging, engineering, physics, etc., where the input-output system is a subject of interest. Namely, the system where one observes the output and is interested in recovering the input signal from... more
There are a large number of problems in imaging, engineering, physics, etc., where the input-output system is a subject of interest. Namely, the system where one observes the output and is interested in recovering the input signal from the available data. The so-called deconvolution problem is the one which is frequently used in many elds. This type of relationships between
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In this article a new nonparametric density estimator based on the sequence of asymmetric kernels is proposed. This method is natural when estimating an unknown density function of a positive random variable. The rates of Mean Squared... more
In this article a new nonparametric density estimator based on the sequence of asymmetric kernels is proposed. This method is natural when estimating an unknown density function of a positive random variable. The rates of Mean Squared Error, Mean Integrated Squared Error, and the L1-consistency are investigated. Simulation studies are conducted to compare a new estimator and its modified version
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this report we discuss only the first part of the project. The second one is concerned with the weak convergence results for the likelihood ratio process, while the third part will be devoted to the different sort of estimators b G of a... more
this report we discuss only the first part of the project. The second one is concerned with the weak convergence results for the likelihood ratio process, while the third part will be devoted to the different sort of estimators b G of a change set without the total boundedness assumption on C.
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An unknown moment-determinate cumulative distribution function or its density function can be recovered from corresponding moments and estimated from the empirical moments. This method of estimating an unknown density is natural in... more
An unknown moment-determinate cumulative distribution function or its density function can be recovered from corresponding moments and estimated from the empirical moments. This method of estimating an unknown density is natural in certain inverse estimation models like multiplicative censoring or biased sampling when the moments of unobserved distribution can be estimated via the transformed moments of the observed distribution. In this paper, we introduce a new nonparametric estimator of a probability density function defined on the positive real line, motivated by the above. Some fundamental properties of proposed estimator are studied. The comparison with traditional kernel density estimator is discussed.
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ABSTRACT The problem of recovering the multivariate probability density function ff from the moments of its Radon transform RfRf is studied. The approximation of the Radon transform RfRf itself is obtained from the moments of ff. Under... more
ABSTRACT The problem of recovering the multivariate probability density function ff from the moments of its Radon transform RfRf is studied. The approximation of the Radon transform RfRf itself is obtained from the moments of ff. Under the mild conditions on ff the uniform rates of convergence for the proposed constructions are established.
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In this paper the well-known insurance ruin problem is reconsidered. The ruin probability is estimated in the case of an unknown claims density, assuming a sample of claims is given. An important step in the construction of the estimator... more
In this paper the well-known insurance ruin problem is reconsidered. The ruin probability is estimated in the case of an unknown claims density, assuming a sample of claims is given. An important step in the construction of the estimator is the application of a regularized version of the inverse of the Laplace transform. A rate of convergence in probability for the integrated squared error (ISE) is derived and a simulation study is included.
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ABSTRACT An unknown probability cumulative distribution function (CDF) can be recovered from its moments and estimated from its empirical moments. In this paper, some further results for such moment-empirical CDFs’ are considered, in... more
ABSTRACT An unknown probability cumulative distribution function (CDF) can be recovered from its moments and estimated from its empirical moments. In this paper, some further results for such moment-empirical CDFs’ are considered, in particular for certain models where the sample is not directly drawn from the distribution of actual interest, as in biased sampling.
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ABSTRACT Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the... more
ABSTRACT Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non‐traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment‐recovered approaches with their counterparts derived by using the histogram and kth nearest neighbour constructions. In addition, one worked example is briefly discussed.
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We present the first results from a new population study of the radio pulsar content in globular clusters. Our goal is to develop a set of publicly available tools to constrain the underlying population distribution functions based on the... more
We present the first results from a new population study of the radio pulsar content in globular clusters. Our goal is to develop a set of publicly available tools to constrain the underlying population distribution functions based on the sample of 140 pulsars in 26 clusters. In this work, we will present our main statistical techniques and apply them to