Asymptotically Unbiased Estimates of a Distribution Function in Dose Effect Relationships

Verfasser / Beitragende:
[M. Tikhov, I. Dolgih]
Ort, Verlag, Jahr:
2015
Enthalten in:
Journal of Mathematical Sciences, 205/1(2015-02-01), 113-120
Format:
Artikel (online)
Online Zugang:
Get it Online (National Licence)
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024 7 0 |a 10.1007/s10958-015-2236-5  |2 doi 
035 |a (NATIONALLICENCE)springer-10.1007/s10958-015-2236-5 
245 0 0 |a Asymptotically Unbiased Estimates of a Distribution Function in Dose Effect Relationships  |h [Elektronische Daten]  |c [M. Tikhov, I. Dolgih] 
520 3 |a A random dose U is injected in a biological organism. Let X be the lower bound, from which response (effect) A random dose U is injected in a biological organism. Let X be the lower bound, from which response (effect) may be registered: if X  X}. The considered characteristic is a regression of W on U, i.e. conditional mathematical expectation E(W|U = x). If injected random dose U and lower bound X are independent, then E(W|U = x) = F(x), where F(x) is a distribution function of random variable X; hence the estimate of unknown distribution function F(x) may be constructed in the form of kernel regression estimate. If U and X are dependent, then conditional mathematical expectation E(W|U = x) = F(x) = P(X < x|U = x) = F(x|u) = T(x) is a conditional distribution function, which in case of studying toxic substances is called the toxicity function. For independent random variables (U,X) function T (x) = F(x) is monotonically nondecreasing. If U and X are dependent, then T (x) takes values from the interval [0, 1], but may be decreasing for some x. Such toxicity functions are called paradoxical — increasing the dose for some values leads to reduction of the effect. Real toxicity functions are quite often paradoxical: in the beginning, increasing the dose of injected substance leads to a growth in the effect; then with increasing of dose the effect diminishes, and then with further increasing of injected dose the effect grows again. We consider the case of independent random variables and study asymptotic behavior of estimates for F(x), although proposed estimates may also be used for paradoxical case. 
540 |a Springer Science+Business Media New York, 2015 
700 1 |a Tikhov  |D M.  |u Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia  |4 aut 
700 1 |a Dolgih  |D I.  |u Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia  |4 aut 
773 0 |t Journal of Mathematical Sciences  |d Springer US; http://www.springer-ny.com  |g 205/1(2015-02-01), 113-120  |x 1072-3374  |q 205:1<113  |1 2015  |2 205  |o 10958 
856 4 0 |u https://doi.org/10.1007/s10958-015-2236-5  |q text/html  |z Onlinezugriff via DOI 
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900 7 |a Metadata rights reserved  |b Springer special CC-BY-NC licence  |2 nationallicence 
908 |D 1  |a research-article  |2 jats 
949 |B NATIONALLICENCE  |F NATIONALLICENCE  |b NL-springer 
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950 |B NATIONALLICENCE  |P 700  |E 1-  |a Tikhov  |D M.  |u Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia  |4 aut 
950 |B NATIONALLICENCE  |P 700  |E 1-  |a Dolgih  |D I.  |u Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia  |4 aut 
950 |B NATIONALLICENCE  |P 773  |E 0-  |t Journal of Mathematical Sciences  |d Springer US; http://www.springer-ny.com  |g 205/1(2015-02-01), 113-120  |x 1072-3374  |q 205:1<113  |1 2015  |2 205  |o 10958 

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