Nonparametric checks for single-index models

By Winfried Stute, Lixing Zhu. 2005

175 citations recorded by the source corpus.

In this paper we study goodness-of-fit testing of single-index models. The large sample behavior of certain score-type test statistics is investigated. As a by-product, we obtain asymptotically distribution-free maximin tests for a large class of local alternatives. Furthermore, characteristic function based goodness-of-fit tests are proposed which are omnibus and able to detect peak alternatives. Simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes. Applications to two real data sets are illustrated.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e7919320c573e5aca181a7dc9bc3d5eb01918f4c

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Citations in the corpus

Empirical likelihood confidence regions in a partially linear single‐index model (2006, methodology): “E-mail: lzhu@hkbu.edu.hk (1994), Speckman (1988), Härdle et al. (1993) and Stute and Zhu (2005).”
Partial linear single index models with distortion measurement errors (2013, methodology): “We further used the test proposed by Stute and Zhu (2005) to check whether ĝ(·) has appropriately fitted this data set.”
Estimation for a partial-linear single-index model (2009, methodology): “Theorem 3 implies that our estimator for β0 has a smaller limiting variance than the estimators in Xia and Härdle (2006) and Carroll et al. (1997).”
Asymptotics for sliced average variance estimation (2007, methodology): “ESTIMATION1 By Yingxing Li and Li-Xing Zhu”
An updated review of Goodness-of-Fit tests for regression models (2013, unknown): “For instance, Stute and Zhu (2005a) propose a scoretype test for H0SIM, which detects Pitman alternatives at a √ n-rate, and also peak alternatives, being undetectable for the previous tests, as discussed in Horowitz and Spokoiny (2001).”
Breaking the curse of dimensionality in nonparametric testing (2008, methodology): “The wild bootstrap, initially proposed by Wu (1986), is often used in smooth tests to compute small sample critical values, see e.”
Testing Conditional Independence via Rosenblatt Transforms (2009, methodology): “Assumption 2(ii) is analogous to Condition A(i) in Theorem 2.1 of Stute and Zhu (2005) or A2 of Delgado and González Manteiga (2001) on page 1475.”