Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in t...

In regression with a high-dimensional predictor vector, it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response. Using the Fourier transform, we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively. Under the normality assumption of the predicto...

The central mean and central subspaces of generalized multiple index model are the main inference targets of sufficient dimension reduction in regression. In this article, we propose an integral transform (ITM) method for estimating these two subspaces. Applying the ITM method, estimates are derived, separately, for two scenarios: (i) No distributional assumptions are imposed on the predictors,...

We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean function and smoothing is not required. The general approach is based on sufficient dimension reduction, the idea being to replace the predictor vector with a lower...

Bentonite is a native, colloidal, hydrated aluminum silicate. It occurs as a very fine, odorless, pale buff or cream-colored powder, free from grit, and has a slightly earthy taste. Although it is insoluble in water, it swells to approximately 12 times its volume when added to water. Bentonite magma is prepared by adding 50 gm. of bentonite to a sufficient quantity of purified water to make 1 l...

We investigate the estimation efficiency of the central mean subspace in the framework of sufficient dimension reduction. We derive the semiparametric efficient score and study its practical applicability. Despite the difficulty caused by the potential high dimension issue in the variance component, we show that locally efficient estimators can be constructed in practice. We conduct simulation ...

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Rand Corporation, Pittsburgh, PA 15213 e-mail: [email protected] Abstract: Many sufficient dimension reduction methodologies for univariate regression have been extended to multivariate regression. Sliced average variance estimation (SAVE) has the potential to recover more reductive information, and recent development enables us to test the dimension and predictor effects with distributions comm...

The central subspace and central mean subspace are two important targets of sufficient dimension reduction. We propose a weighted chi-squared test to determine their dimensions based on matrices whose column spaces are exactly equal to the central subspace or the central mean subspace. The asymptotic distribution of the test statistic is obtained. Simulation examples are used to demonstrate the...