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Goodness-of-fit criteria based on test statistics {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x). Investigation of power of one-sided criterion for large n; Kriterii soglasiya, osnovannye na proverochnoj statistiks {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x); Issledovanie moshchnosti odnostoronnego kriteriya dlya bol`shikh n

Technical Report:

Abstract

The main properties of new integral nonparametric goodness-of-fit criterion {omega}{sub n}{sup 3} for large emperical samples sizes are considered. Its comparison with familiar {omega}{sub n}{sup 2} criterion and with Watson`s criterion U-bar (connected with another integral criterion {omega}{sub n}{sup 1}) in frames of Chapman`s approach for n=50, 200 and 1000 was performed. For alternative hypotheses, minimizing the power, an advantage of the {omega}{sub n}{sup 3} in a sufficient broad range of significance level a and, what is specially important for practical applications, for small values was shown. It was also shown that for hypotheses, maximizing the power, the Watson`s criterion has a slight advantage over {omega}{sub n}{sup 3} criterion. The analytical expressions allowing to evaluate the power of {omega}{sub n}{sup 3} criterion for arbitrary one-sided alternative hypotheses are presented. 9 refs.; 5 figs.
Publication Date:
Dec 31, 1992
Product Type:
Technical Report
Report Number:
JINR-R-11-92-409
Reference Number:
SCA: 990200; PA: AIX-25:007019; EDB-94:016807; ERA-19:007923; NTS-94:014839; SN: 94001126753
Resource Relation:
Other Information: PBD: 1992
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CHAPMAN-KOLMOGOROV EQUATION; ANALYTICAL SOLUTION; STATISTICS; DISPERSION RELATIONS; DISTRIBUTION FUNCTIONS; MONTE CARLO METHOD; SIMULATION; 990200; MATHEMATICS AND COMPUTERS
OSTI ID:
10113109
Research Organizations:
Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Computing Techniques and Automation
Country of Origin:
JINR
Language:
Russian
Other Identifying Numbers:
Other: ON: DE94611059; TRN: RU9305420007019
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
22 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Zrelov, P V, and Ivanov, V V. Goodness-of-fit criteria based on test statistics {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x). Investigation of power of one-sided criterion for large n; Kriterii soglasiya, osnovannye na proverochnoj statistiks {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x); Issledovanie moshchnosti odnostoronnego kriteriya dlya bol`shikh n. JINR: N. p., 1992. Web.
Zrelov, P V, & Ivanov, V V. Goodness-of-fit criteria based on test statistics {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x). Investigation of power of one-sided criterion for large n; Kriterii soglasiya, osnovannye na proverochnoj statistiks {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x); Issledovanie moshchnosti odnostoronnego kriteriya dlya bol`shikh n. JINR.
Zrelov, P V, and Ivanov, V V. 1992. "Goodness-of-fit criteria based on test statistics {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x). Investigation of power of one-sided criterion for large n; Kriterii soglasiya, osnovannye na proverochnoj statistiks {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x); Issledovanie moshchnosti odnostoronnego kriteriya dlya bol`shikh n." JINR.
@misc{etde_10113109,
title = {Goodness-of-fit criteria based on test statistics {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x). Investigation of power of one-sided criterion for large n; Kriterii soglasiya, osnovannye na proverochnoj statistiks {omega}{sub n}{sup 3} = n{sup 3/2} {sub -{infinity}} integral {sup {infinity}} [S{sub n}(x) - F(x)]{sup 3}dF(x); Issledovanie moshchnosti odnostoronnego kriteriya dlya bol`shikh n}
author = {Zrelov, P V, and Ivanov, V V}
abstractNote = {The main properties of new integral nonparametric goodness-of-fit criterion {omega}{sub n}{sup 3} for large emperical samples sizes are considered. Its comparison with familiar {omega}{sub n}{sup 2} criterion and with Watson`s criterion U-bar (connected with another integral criterion {omega}{sub n}{sup 1}) in frames of Chapman`s approach for n=50, 200 and 1000 was performed. For alternative hypotheses, minimizing the power, an advantage of the {omega}{sub n}{sup 3} in a sufficient broad range of significance level a and, what is specially important for practical applications, for small values was shown. It was also shown that for hypotheses, maximizing the power, the Watson`s criterion has a slight advantage over {omega}{sub n}{sup 3} criterion. The analytical expressions allowing to evaluate the power of {omega}{sub n}{sup 3} criterion for arbitrary one-sided alternative hypotheses are presented. 9 refs.; 5 figs.}
place = {JINR}
year = {1992}
month = {Dec}
}