The Minimum Distance Estimation with Multiple Integral in Panel Data

This paper studies the minimum distance estimation problem for panel data model. We propose the minimum distance estimators of regression parameters of the panel data model and investigate their asymptotic distributions. This paper contains two main contributions. First, the domain of application of the minimum distance estimation method is extended to the panel data model. Second, the proposed estimators are more efficient than other existing ones. Simulation studies compare performance of the proposed estimators with performance of others and demonstrate some superiority of our estimators.Comment: Minimum distance estimation; panel dat

Supplement to "Comparison of Misspecified Calibrated Models"

This paper contains supplemental material to Hnatkovska, Marmer, and Tang (2009) "Comparison of Misspecified Calibrated Models: The Minimum Distance Approach".misspecified models; calibration; minimum distance estimation

Lattice polytopes in coding theory

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.Comment: 11 pages, 3 figure

Asymptotics in Minimum Distance from Independence Estimation

In this paper we introduce a family of minimum distance from independence estimators, suggested by Manski's minimum mean square from independence estimator. We establish strong consistency, asymptotic normality and consistency of resampling estimates of the distribution and variance of these estimators. For Manski's estimator we derive both strong consistency and asymptotic normality.Donsker class, empirical processes, extremum estimator, nonlinear simultaneous equations models, resampling estimators

Minimum local distance density estimation

We present a local density estimator based on first-order statistics. To estimate the density at a point, x, the original sample is divided into subsets and the average minimum sample distance to x over all such subsets is used to define the density estimate at x. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.United States. Department of Energy. Applied Mathematical Sciences Program (Award DE-FG02-08ER2585)United States. Department of Energy. Applied Mathematical Sciences Program (Award de-sc0009297

Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild assumptions, are asymptotically normal with variance-covarince matrix equal to the Cramer-Rao bound.Comment: Minor revision, some references and remarks adde

Weighted Minimum Mean-Square Distance from Independence Estimation

In this paper we introduce a family of semi-parametric estimators, suggested by Manski's minimum mean-square distance from independence estimator. We establish the strong consistency, asymptotic normality and consistency of bootstrap estimates of the sampling distribution and the asymptotic variance of these estimators.Semiparametric estimation, simultaneous equations models, empirical processes, extremum estimators

Partial mixture model for tight clustering of gene expression time-course

Background: Tight clustering arose recently from a desire to obtain tighter and potentially more informative clusters in gene expression studies. Scattered genes with relatively loose correlations should be excluded from the clusters. However, in the literature there is little work dedicated to this area of research. On the other hand, there has been extensive use of maximum likelihood techniques for model parameter estimation. By contrast, the minimum distance estimator has been largely ignored. Results: In this paper we show the inherent robustness of the minimum distance estimator that makes it a powerful tool for parameter estimation in model-based time-course clustering. To apply minimum distance estimation, a partial mixture model that can naturally incorporate replicate information and allow scattered genes is formulated. We provide experimental results of simulated data fitting, where the minimum distance estimator demonstrates superior performance to the maximum likelihood estimator. Both biological and statistical validations are conducted on a simulated dataset and two real gene expression datasets. Our proposed partial regression clustering algorithm scores top in Gene Ontology driven evaluation, in comparison with four other popular clustering algorithms. Conclusion: For the first time partial mixture model is successfully extended to time-course data analysis. The robustness of our partial regression clustering algorithm proves the suitability of the ombination of both partial mixture model and minimum distance estimator in this field. We show that tight clustering not only is capable to generate more profound understanding of the dataset under study well in accordance to established biological knowledge, but also presents interesting new hypotheses during interpretation of clustering results. In particular, we provide biological evidences that scattered genes can be relevant and are interesting subjects for study, in contrast to prevailing opinion