Download Free On The Finite Sample Properties Of Regularized M Estimators Book in PDF and EPUB Free Download. You can read online On The Finite Sample Properties Of Regularized M Estimators and write the review.

We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. The concentration rate exhibits a “variance-bias” trade-off, with the “variance” term being governed by a novel measure of the “size” of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the “(squared) bias” and “variance” terms. We illustrate the results with several canonical examples of, both, non-parametric and high-dimensional models.
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. Our results exhibit a variance-bias trade-off, with the variance term being governed by a novel measure of the complexity of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the (squared) bias and variance terms. We illustrate the results with several canonical examples.
Excerpt from Finite Sample Properties of Some Alternative Gmm Estimators Let vtw) denote (an infeasible) consistent estimator of this covariance matrix. This latter estimator is typically made operational by substituting a consistent estimator for (3. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This book is a collection of articles that present the most recent cutting edge results on specification and estimation of economic models written by a number of the world’s foremost leaders in the fields of theoretical and methodological econometrics. Recent advances in asymptotic approximation theory, including the use of higher order asymptotics for things like estimator bias correction, and the use of various expansion and other theoretical tools for the development of bootstrap techniques designed for implementation when carrying out inference are at the forefront of theoretical development in the field of econometrics. One important feature of these advances in the theory of econometrics is that they are being seamlessly and almost immediately incorporated into the “empirical toolbox” that applied practitioners use when actually constructing models using data, for the purposes of both prediction and policy analysis and the more theoretically targeted chapters in the book will discuss these developments. Turning now to empirical methodology, chapters on prediction methodology will focus on macroeconomic and financial applications, such as the construction of diffusion index models for forecasting with very large numbers of variables, and the construction of data samples that result in optimal predictive accuracy tests when comparing alternative prediction models. Chapters carefully outline how applied practitioners can correctly implement the latest theoretical refinements in model specification in order to “build” the best models using large-scale and traditional datasets, making the book of interest to a broad readership of economists from theoretical econometricians to applied economic practitioners.
This dissertation is composed of three essays regarding the finite sample properties of estimators for nonparametric models. In the first essay we investigate the finite sample performances of four estimators for additive nonparametric regression models - the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this essay. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared errors (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods. We compare the estimators' performances based on various bandwidth selection procedures that are currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study. The second essay is concerned with some recently proposed kernel estimators for panel data models. These estimators include the local linear estimator, the quasi-likelihood estimator, the pre-whitening estimators, and the marginal kernel estimator. We focus on the finite sample properties of the above mentioned estimators on random effects panel data models with different within-subject correlation structures. For each estimator, we use the asymptotic mean average squared errors (AMASE) as the criterion function to select the bandwidth. The relative performance of the test estimators are compared based on their average squared errors, average biases and variances. The third essay is concerned with the finite sample properties of estimators for nonparametric regression models with autoregressive errors. The estimators studied are: the local linear, the quasi-likelihood, and two pre-whitening estimators. Bandwidths are selected based on the minimization of the asymptotic mean average squared errors (AMASE) for each estimator. Two regression functions and multiple variants of autoregressive processes are employed in the simulation. Comparison of the relative performances is based mainly on the estimators' average squared errors (ASE). Our ultimate objective is to provide an extensive finite sample comparison among competing estimators with a practically selected bandwidth.