Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

The jensen-shannon divergence

Abstract: In this paper we investigate the Jensen-Shannon parametric divergence for testing goodness-of-fit for point estimation. Most of the work presented is an analytical study of the asymptotic differences between different members of the family proposed in goodness of fit, together with an examination of closer approximations to the exact distribution of these statistics than the commonly used chi-squared distribution. Finally the minimum Jensen-Shannon divergence estimates are introduced and compared with other well-known estimators by computer simulation.

Monte Carlo EM for missing covariates in parametric regression models.

Abstract: We propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates. We allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout. When the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association85, 765–769). We extend this method t o continuous or mixed categorical and continuous covariates, and for arbitrary parametric regression models, by adapting a Monte Carlo version of the EM algorithm as discussed by Wei and Tanner (1990, Journal of the American Statistical Association85, 699–704). In addition, we discuss the Gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log‐concave. The log‐concavity property of the conditional distributions will facilitate a straightforward implementation of the Gibbs sampler via the adaptive rejection algorithm of Gilks and Wild (1992, Applied Statistics41, 337–348). We assume the model for the response given the covariates is an arbitrary parametric regression model, such as a generalized linear model, a parametric survival model, or a nonlinear model. We model the marginal distribution of the covariates as a product of one‐dimensional conditional distributions. This allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the E‐step. We present examples involving both simulated and real data.

Timing yield estimation from static timing analysis

Abstract: This paper presents a means for estimating parametric timing yield and guiding robust design for-quality in the presence of manufacturing and operating environment variations. Dual emphasis is on computational efficiency and providing meaningful robust-design guidance. Computational efficiency is achieved by basing the proposed methodology on a post-processing step applied to the report generated as a by-product of static timing analysis. Efficiency is also ensured by exploiting the fact that for small processing/environment variations, a linear model is adequate for capturing the resulting delay change. Meaningful design guidance is achieved by analyzing the timing-related influence of variations on a path-by-path basis, allowing designers perform a quality-oriented design pass focused on key paths. A coherent strategy is provided to handle both die-to-die and within-die variations. Examples from a PowerPC microprocessor illustrate the methodology and its capabilities.

Directional derivatives of the solution of a parametric nonlinear program

Abstract: Consider a parametric nonlinear optimization problem subject to equality and inequality constraints. Conditions under which a locally optimal solution exists and depends in a continuous way on the parameter are well known. We show, under the additional assumption of constant rank of the active constraint gradients, that the optimal solution is actually piecewise smooth, hence B-differentiable. We show, for the first time to our knowledge, a practical application of quadratic programming to calculate the directional derivative in the case when the optimal multipliers are not unique.