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Teoriya Veroyatnostei i ee Primeneniya, 1978, Volume 23, Issue 2, Pages 263–274
(Mi tvp3035)
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This article is cited in 2 scientific papers (total in 2 papers)
Goodness-of-fit tests based on a measure of divergency between two scalar products
O. V. Gerleĭna, R. Pincusb a Tula
b Berlin
Abstract:
Let $X_1,\dots,X_n$ be independent random variables with values in $(\mathfrak X, \mathfrak A)$ identically distributed according to a measure $P$ and let $\varphi_1,\dots,\varphi_k$ be functions on $(\mathfrak X, \mathfrak A)$ square integrable with respect to $P$. The asymptotic distribution (as $n\to\infty$) of certain tests of hypotheses on values of the functionals $\pi_1(P)=\mathbf E_P\varphi_1,\dots,\pi_k(P)=\mathbf E_P\varphi_k$ is investigated. The tests under consideration depend only on the values of the statistics $\displaystyle\overline\varphi_1=\frac{1}{n}\sum_{\nu=1}^n\varphi_1(X_\nu)\dots$,
$\displaystyle\overline\varphi_k=\frac{1}{n}\sum_{\nu=1}^n\varphi_k(X_\nu)$and are based on a measure of divergency between the two scalar products introduced in [4].
Received: 25.12.1975
Citation:
O. V. Gerleǐn, R. Pincus, “Goodness-of-fit tests based on a measure of divergency between two scalar products”, Teor. Veroyatnost. i Primenen., 23:2 (1978), 263–274; Theory Probab. Appl., 23:2 (1979), 248–258
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https://www.mathnet.ru/eng/tvp3035 https://www.mathnet.ru/eng/tvp/v23/i2/p263
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