Nonparametric estimators of probability characteristics using unbiased prior conditions

Dmitriev, Yury; Кошкин, Г. М.

doi:10.1007/s00362-018-1044-7

Cited by 11 publications

(8 citation statements)

References 11 publications

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“…The aprioristic information (formula ( 9)) allows us to consider a wide range of information about   , G  quantitative and qualitative in character. 16,17 Taking into account aprioristic information (9), a modified nonparametric estimate of the Rosenblatt-Parzen density 16,17  …”

Section:  mentioning

confidence: 99%

Semiparametric and semi-nonparametric estimates of the kinetic energy in the atmospheric boundary layer from minisodar measurements

Simakhin

Потекаев²,

Cherepanov³

et al. 2022

28th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics

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Based on the semiparametric and semi-nonparametric algorithms developed by the authors, the kinetic energies of outliers and ordered air motion are estimated by post-processing of minisodar measurements of 3D wind vector and its 3D variance in the lower 200-meter layer of the atmosphere. A nonmonotonic increase in the kinetic energy of the outliers with sounding altitude is established, which can be explained by the nonmonotonic increase of the turbulent kinetic energy of local atmospheric vortices.

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Section:  mentioning

confidence: 99%

Semiparametric and semi-nonparametric estimates of the kinetic energy in the atmospheric boundary layer from minisodar measurements

Simakhin

Потекаев²,

Cherepanov³

et al. 2022

28th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics

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“…This estimate is asymptotically unbiased and normal. Its variance is determined by the formula [12]: (10) where (11) Moreover, it is easy to verify using formula (10) that (12) Hence, it is obvious that and thus due to asymptotic unbiasedness for sufficiently large volumes of observations, the use of additional information about the known quantile leads to a decrease in the mean squared error (MSE) normalized to N: (13) and hence, to improve the accuracy of estimating the average volume of demand. Here a = EX.…”

Section: Economic Order Quantity With Additional Information About Thmentioning

confidence: 99%

“…Note that in this case trade is also considered as production. Therefore, in modern logistics, in order to search for the best estimate of potential demand, all kinds of mathematical models of various levels of complexity [5][6][7][8] are used, including those that involve additional information to reduce the forecasting error and improve the quality of assessment [9][10][11] and product classification [6,12]. This paper proposes a new, more accurate method for calculating the economic order size and its confidence intervals using additional information about the quantile of the sales volume cumulative distribution function (CDF).…”

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confidence: 99%

“…Restrictive parameters are also taken into account, for example, the maximum volume of the warehouse and the observed frequency of cases of its overflow. Usually such knowledge is ignored, although it can be used to advantage, since it has long been known that additional information helps to improve the quality of statistical procedures [6][7][8][9][10][11][12][13]. It is also worth noting that the use of information about the quantile has already been considered in a number of works [13][14][15][16][17][18], using the method of projecting the estimate of the distribution function into an a priori class.…”

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confidence: 99%

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The economic order quantity taking into account additional information about the known quantile of the cumulative distribution function of the product’s sales volume

Zenkova¹,

Musoni²

2020

Bus. Inform.

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In modern logistics and supply chain management, the task of inventory management is paramount. The total costs of the enterprise and consequently, its profit, directly depend on the accuracy of calculating the volumes and terms of orders. In this work, the problem of increasing the accuracy of calculating the economic order quantity for a product was solved by involving additional information about the known quantile of a given level of the distribution function of the volume of product's demand. The quantile information was used to recalculate the annual demand for the product, based on a modified estimator of the sales expectation for the period. The modified estimator is asymptotically unbiased, normal, and more accurate than the traditional sample mean in the sense of mean squared error. New formulas for calculating the economic order quantity and its confidence interval were presented and tested on real data on the monthly sales volumes of goods of a large retail store network over two years. It is shown that the classic way of mean calculation led to an underestimation of the volume of the economic order quantity, which in turn increased the risk of a shortage, and hence a drop in the quality of logistics services. The new calculation method also showed that the period between orders should be one day shorter. The work is practically significant; according to its results, recommendations are given to the enterprise.

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“…EX a  (6) The estimator by making use of such information according to [8][9][10][11][12][13][14][15][16][17] can be taken in the following form:…”

Section: Construction Of Estimators Using Expected Lifetimementioning

confidence: 99%

Estimation of present value of whole life annuity using information about expectation of life

Dmitriev¹,

Кошкин²

2018

Tomsk State University Journal of Control and Computer Science

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The paper deals with the estimation problem of the actuarial present value of the continuous whole life annuity using auxiliary information about the expectation of life. Nonparametric estimators of life annuity are constructed by individuals' death moments. It is shown that the usage of such auxiliary information can often provide the mean squared error (MSE) smaller than that of standard estimators. An adaptive estimator is also proposed. The asymptotic normality of all these estimators is proved.

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Nonparametric estimators of probability characteristics using unbiased prior conditions

Cited by 11 publications

References 11 publications

Semiparametric and semi-nonparametric estimates of the kinetic energy in the atmospheric boundary layer from minisodar measurements

Semiparametric and semi-nonparametric estimates of the kinetic energy in the atmospheric boundary layer from minisodar measurements

The economic order quantity taking into account additional information about the known quantile of the cumulative distribution function of the product’s sales volume

Estimation of present value of whole life annuity using information about expectation of life

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