Almost Sure Invariance Principles for Partial Sums of Mixing $B$-Valued Random Variables

Kuelbs, J.; Philipp, Walter

doi:10.1214/aop/1176994565

Cited by 148 publications

(91 citation statements)

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“…Theorem 4 of Kuelbs and Philipp [21] implies that Condition A holds with rate T Q, 1/4<~<1/2, and we get the following result: We considered only processes of runs down but with the same method we can develop strong approximations of processes of other types of runs (runs up, runs down or up, and turning points). EXAMPLE 5.…”

Section: S(t)=~y~ and N(t)=n([t])mentioning

confidence: 73%

Strong approximations of renewal processes and their applications

Horváth

1986

Acta Math Hung

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Section: S(t)=~y~ and N(t)=n([t])mentioning

confidence: 73%

Strong approximations of renewal processes and their applications

Horváth

1986

Acta Math Hung

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“…For instance, Kuelbs and Philipp (1980) imposes strong mixing condition and is subject to the Ling (2007)'critique regarding the backward sum. On the other hand, Ling relaxes the mixing condition but add the martingale di¤erence assumption on g t , developing a strong approximation results for the backward sum as well as the forward sum.…”

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confidence: 99%

Testing for structural stability in the whole sample

Hidalgo

Seo

2013

Journal of Econometrics

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The paper examines a Lagrange Multiplier type test for the constancy of the parameter in general models with dependent data without imposing any artificial choice of the possible location of the break. In order to prove the asymptotic behaviour of the test, we extend a strong approximation result for partial sums of a sequence of random variables. We also present a Monte-Carlo experiment to examine the finite sample performance of the test and how it compares with tests which assume some knowledge of the possible location of the break..

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“…Proof. For fixed designs by adopting arguments similar to that in the proof of Lemma 1 in Eubank and Speckman [5] , it follows easily from the strong approximation of α-mixing sequence in Kuels and Philipp [11] . Next we prove that this lemma holds for random designs.…”

Section: Lemma 52 Suppose That Conditions (A1)-(a3) and (J) Or (B1)mentioning

confidence: 99%

Confidence Intervals of Variance Functions in Generalized Linear Model

Zhou

2006

Acta Math. Appl. Sin, Engl. Ser.

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In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respectively. Bias-corrected confidence bands are proposed for the (conditional) variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the (conditional) variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparametric autoregressive times series model with heteroscedastic conditional variance.

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Almost Sure Invariance Principles for Partial Sums of Mixing $B$-Valued Random Variables

Cited by 148 publications

References 0 publications

Strong approximations of renewal processes and their applications

Strong approximations of renewal processes and their applications

Testing for structural stability in the whole sample

Confidence Intervals of Variance Functions in Generalized Linear Model

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