Regression estimate of the multidimensional probability density and its properties

“…The nonparametric estimate p(x) of the probability density has the property of asymptotic convergence to p(x) [11]. From the condition of a minimum asymptotic expression for the MSD of p(x) from p(x), we obtain a procedure for optimal choice of the number of sampling intervals [12]: (2) which is determined by the form of the probability density to be recovered, its domain of definition Δ, and the volume n of initial statistical data.…”

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confidence: 99%

“…As an approximation with respect to the empirical data V 1 for the desired probability density p(x), we take the nonparametric estimate [11]:…”

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confidence: 99%

“…Two-level nonparametric systems have been developed for solving two-and multialternative classification problems, and the asymptotic properties of estimates of the equations of separating surfaces for the univariate and multivariate cases have been established [4][5][6][7][8]. The problem of large samples can be avoided by using a nonparametric estimate of the probability density, the synthesis of which is based on compressing the initial statistical data [9][10][11]. The condition of a minimum asymptotic expression for its mean square deviation (MSD) is used to determine a procedure for optimal choice of the number of sampling intervals in the range of variation of the random variable [12].…”

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confidence: 99%

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Comparison of the Effectiveness of Methods for Sampling the Range of Variation of Random Quantities in Synthesis of Nonparametric Estimates of Probability Density

Лапко

2014

Meas Tech

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The approximation properties of a nonparametric estimate of probability density are studied for different methods of sampling the domain of definition. The indicators of the effectiveness of these methods are estimated. Keywords: nonparametric estimate of probability density, approximation properties, sampling methods, normal distribution law.The computational efficiency of nonparametric algorithms for data processing are determined by the amount of statistical data and decrease with increasing amounts of data. Under these conditions, it is appropriate to use both the principles of decomposition of the initial statistical data based on their volume and parallel computing. A mixture of nonparametric estimates of the probability densities for univariate and multivariate random quantities has been proposed and studied [1, 2]. It has a considerably smaller dispersion than the traditional Rosenblatt-Parzen estimate of the probability density [3]. The reduction in computational time is comparable to the number of components of the mixture of nonparametric probability density estimates.These results have been generalized for estimating the resolving function in the problem of pattern recognition under large sample conditions. Two-level nonparametric systems have been developed for solving two-and multialternative classification problems, and the asymptotic properties of estimates of the equations of separating surfaces for the univariate and multivariate cases have been established [4][5][6][7][8]. The problem of large samples can be avoided by using a nonparametric estimate of the probability density, the synthesis of which is based on compressing the initial statistical data [9][10][11]. The condition of a minimum asymptotic expression for its mean square deviation (MSD) is used to determine a procedure for optimal choice of the number of sampling intervals in the range of variation of the random variable [12].Here an analysis of the approximation properties of a nonparametric estimate of the probability density is used to compare the most widespread procedures for sampling the range of variation of normally distributed random quantities.Synthesis of a Nonparametric Estimate of the Probability Density. Consider a sample V = (x i , i =⎯⎯⎯ 1, n) of n independent values of a univariate random quantity x with an unknown probability density p(x). We divide the region over which p(x) is to be determined into N nonintersecting intervals of length 2β and form a set of random quantities X j , j =⎯⎯⎯ 1, n. As the

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“…At the proof of the theorem the technique offered in work [3] and developed in [4][5][6][7][8] is used.…”

Section: Properties Of Nonparametric Estimates Of the Probability Denmentioning

confidence: 99%

Testing of hypothesis of two-dimensional random variables independence on the basis of algorithm of pattern recognition

Лапко

Yuronen

2016

IOP Conf. Ser.: Mater. Sci. Eng.

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Regression estimate of the multidimensional probability density and its properties

Cited by 24 publications

References 1 publication

Testing of hypothesis o f random variables independence on the basis of nonparametric algorithm of pattern recognition

Testing of hypothesis o f random variables independence on the basis of nonparametric algorithm of pattern recognition

Comparison of the Effectiveness of Methods for Sampling the Range of Variation of Random Quantities in Synthesis of Nonparametric Estimates of Probability Density

Testing of hypothesis of two-dimensional random variables independence on the basis of algorithm of pattern recognition

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