In this paper, we apply our inversion mapping method, the trajectory mixture density network (TMDN), to a new corpus of articulatory data, recorded with a Carstens AG500 electromagnetic articulograph. This new data set, mngu0, is relatively large and phonetically rich, among other beneficial characteristics. We obtain good results, with a root mean square (RMS) error of only 0.99mm. This compar...

This paper proposes a trajectory model which is based on a mixture density network trained with target features augmented with dynamic features together with an algorithm for estimating maximum likelihood trajectories which respects constraints between the static and derived dynamic features. This model was evaluated on an inversion mapping task. We found the introduction of the trajectory mode...

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.

Statistical inference procedures are considered when less complete prior information is available than usually considered. For the purposes of this paper, the prior information is taken to be the specification of a set of probability measures 9. With any one prior probability measure the corresponding Bayes’ estimate may be found; the recommended inference procedure when a whole set of prior pr...

In this paper we have suggested difference-type estimator for estimation of population mean of the study variable y in the presence of measurement error using auxiliary information. The optimum estimator in the suggested estimator has been identified along with its mean square error formula. It has been shown that the suggested estimator performs more efficient then other existing estimators. A...

We obtain, for T ε ≤ U = U(T ) ≤ T 1/2−ε, asymptotic formulas for Z 2T T (E(t+ U)− E(t)) dt, Z 2T T (∆(t+ U)−∆(t)) dt, where ∆(x) is the error term in the classical divisor problem, and E(T ) is the error term in the mean square formula for |ζ( 1 2 + it)|. Upper bounds of the form Oε(T 1+εU2) for the above integrals with biquadrates instead of square are shown to hold for T 3/8 ≤ U = U(T ) ≪ T ...

This paper proposes two ratio and product-type estimators using transformation based on known minimum and maximum values of auxiliary variable. The biases and mean squared errors of the suggested estimators are obtained under large sample approximation. Conditions are obtained under which the suggested estimators are superior to the conventional unbiased estimator, usual ratio and product estim...