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.
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}
}
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}
}