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- Yanyuan Ma, Marc G Genton
- 1998

In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the in¯uence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not… (More)

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the… (More)

Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a minimum assumption on the specific regression form, it… (More)

- Yanyuan Ma, Alan Edelman
- 1997

We show that if an 11 X n Jordan block is perturbed by an O(E) upper k-Hessen-berg matrix (k subdiagonals including the main diagonal), then generically the eigenvalues split into p rings of size k and one of size T (if r f O), where n = pk + r. This generalizes the familiar result (k = n, p = 1, r = 0) that generically the eigenvalues split into a ring of… (More)

Treating matrices as points in n 2 dimensional space, we apply geometry to study and explain algorithms for the numerical determination of the Jordan structure of a matrix. Traditional notions such as sensitivity of subspaces are replaced with angles between tangent spaces of manifolds in n 2 dimensional space. We show that the subspace sensitivity is… (More)

- Yanyuan Ma, Marc G Genton
- 2004

We propose a flexible class of skew-symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and… (More)

We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency… (More)

- Peter Hall, Yanyuan Ma
- 2007

We consider functional measurement error models where the measurement error distribution is estimated non-parametrically. We derive a locally efficient semiparametric estima-tor but propose not to implement it owing to its numerical complexity. Instead, a plug-in estimator is proposed, where the measurement error distribution is estimated through… (More)

We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension… (More)

We examine the locally efficient semiparametric estimator proposed by Tsiatis and Ma (2004) in the situation when a sufficient and complete statistic exists. We derive a closed form solution and show that when implemented in generalized linear models with normal measurement error, this estimator is equivalent to the efficient score estimator in Stefanski… (More)