Download or read book Accurate Finite Sample Inference for Generalized Linear Models and Models on Overidentifying Moment Conditions written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Accurate Finite Sample Inference for Generalized Linear Models and Models on Overidentifying Moment Conditions written by Ndame Lô and published by . This book was released on 2006 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical inference in statistic and econometric models is typically carried out by means of asymptotic approximations to the sampling distribution of estimators and test statistics. These approximations often do not provide accurate p-values and confidences intervals, especially when the sample size is small. Moreover, even if the sample size is large, the accuracy can be poor due to model misspecification (nonrobustness). Several alternative techniques have been proposed in the statistic and econometric literature to improve the accuracy of clasical inference. In general, these alternatives address either the accuracy of the first-order approximations or the nonrobustness issue. However, the development of general procedures which are both robust and second order accurate is still an open question. In this thesis, we propose an alternative statistical test wich has both robustness and small sample properties for two large and important classes of models: Generalized Linear Models (GLM) and models on overidentifying moments conditions.

Download or read book Robust and Accurate Inference for Generalized Linear Models written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of generalized linear models, the nonrobustness of classical estimators and tests for the parameters is a well known problem and alternative methods have been proposed in the literature. These methods are robust and can cope with deviations from the assumed distribution. However, they are based on ̄rst order asymptotic theory and their accuracy in moderate to small samples is still an open question. In this paper we propose a test statistic which combines robustness and good accuracy for moderate to small sample sizes. We combine results from Cantoni and Ronchetti (2001) and Robinson, Ronchetti and Young (2003) to obtain a robust test statistic for hypothesis testing and variable selection which is asymptotically Â2¡distributed as the three classical tests but with a relative error of order O(n¡1). This leads to reliable inference in the presence of small deviations from the assumed model distribution and to accurate testing and variable selection even in moderate to small samples.

Download or read book Information Theoretic Approaches to Inference in Moment Condition Models written by Guido Imbens and published by . This book was released on 1995 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-step efficient GMM estimation has been developed in the recent papers of Back and Brown (1990), Imbens (1993) and Qin and Lawless (1994). These papers emphasized methods that correspond to using Owen's (1988) method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates. In this paper we consider an alternative KLIC motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes GMM as a special case. Such KLIC-motivated reweightings introduce M auxiliary `tilting' parameters, where M is the number of moments; parameter and overidentification hypotheses can be recast in terms of these tilting parameters. Such tests, when appropriately conditioned on the estimates of the original parameters, are often startlingly more effective than their conventional counterparts. This is apparently due to the local ancillarity of the original parameters for the tilting parameters.

Download or read book Generalized Method of Moments written by Alastair R. Hall and published by Oxford University Press. This book was released on 2005 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Method of Moments (GMM) has become one of the main statistical tools for the analysis of economic and financial data. This book is the first to provide an intuitive introduction to the method combined with a unified treatment of GMM statistical theory and a survey of recentimportant developments in the field. Providing a comprehensive treatment of GMM estimation and inference, it is designed as a resource for both the theory and practice of GMM: it discusses and proves formally all the main statistical results, and illustrates all inference techniques using empiricalexamples in macroeconomics and finance.Building from the instrumental variables estimator in static linear models, it presents the asymptotic statistical theory of GMM in nonlinear dynamic models. Within this framework it covers classical results on estimation and inference techniques, such as the overidentifying restrictions test andtests of structural stability, and reviews the finite sample performance of these inference methods. And it discusses in detail recent developments on covariance matrix estimation, the impact of model misspecification, moment selection, the use of the bootstrap, and weak instrumentasymptotics.

Download or read book Generalized Method of Moments Estimation written by Laszlo Matyas and published by Cambridge University Press. This book was released on 1999-04-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized method of moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.

Download or read book Maximum Likelihood Estimation and Large sample Inference for Generalized Linear and Nonlinear Regression Models written by Bent Jøgensen and published by . This book was released on 1982 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Second Order Accurate Inference for Generalized Linear Models written by Ndame Lô and published by . This book was released on 2006 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inference and Linear Models written by Donald Alexander Stuart Fraser and published by McGraw-Hill Companies. This book was released on 1979 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Inference for Generalized Linear Models written by Sahar Hosseinian and published by . This book was released on 2009 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Oxford Handbook of Panel Data written by Badi Hani Baltagi and published by . This book was released on 2015 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of Panel Data examines new developments in the theory and applications of panel data. It includes basic topics like non-stationary panels, co-integration in panels, multifactor panel models, panel unit roots, measurement error in panels, incidental parameters and dynamic panels, spatial panels, nonparametric panel data, random coefficients, treatment effects, sample selection, count panel data, limited dependent variable panel models, unbalanced panel models with interactive effects and influential observations in panel data. Contributors to the Handbook explore applications of panel data to a wide range of topics in economics, including health, labor, marketing, trade, productivity, and macro applications in panels. This Handbook is an informative and comprehensive guide for both those who are relatively new to the field and for those wishing to extend their knowledge to the frontier. It is a trusted and definitive source on panel data, having been edited by Professor Badi Baltagi-widely recognized as one of the foremost econometricians in the area of panel data econometrics. Professor Baltagi has successfully recruited an all-star cast of experts for each of the well-chosen topics in the Handbook.

Download or read book Applying Generalized Linear Models written by and published by . This book was released on 1997 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fixed Smoothing Asymptotic Theory in Over identified Econometric Models in the Presence of Time series and Clustered Dependence written by Jungbin Hwang and published by . This book was released on 2016 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the widely used over-identified econometric model, the two-step Generalized Methods of Moments (GMM) estimator and inference, first suggested by Hansen (1982), require the estimation of optimal weighting matrix at the initial stages. For time series data and clustered dependent data, which is our focus here, the optimal weighting matrix is usually referred to as the long run variance (LRV) of the (scaled) sample moment conditions. To maintain generality and avoid misspecification, nowadays we do not model serial dependence and within-cluster dependence parametrically but use the heteroscedasticity and autocorrelation robust (HAR) variance estimator in standard practice. These estimators are nonparametric in nature with high variation in finite samples, but the conventional increasing smoothing asymptotics, so called small-bandwidth asymptotics, completely ignores the finite sample variation of the estimated GMM weighting matrix. As a consequence, empirical researchers are often in danger of making unreliable inferences and false assessments of the (efficient) two-step GMM methods. Motivated by this issue, my dissertation consists of three papers which explore the efficiency and approximation issues in the two-step GMM methods by developing new, more accurate, and easy-to-use approximations to the GMM weighting matrix. The first chapter, "Simple and Trustworthy Cluster-Robust GMM Inference" explores new asymptotic theory for two-step GMM estimation and inference in the presence of clustered dependence. Clustering is a common phenomenon for many cross-sectional and panel data sets in applied economics, where individuals in the same cluster will be interdependent while those from different clusters are more likely to be independent. The core of new approximation scheme here is that we treat the number of clusters G fixed as the sample size increases. Under the new fixed-G asymptotics, the centered two-step GMM estimator and two continuously-updating estimators have the same asymptotic mixed normal distribution. Also, the t statistic, J statistic, as well as the trinity of two-step GMM statistics (QLR, LM and Wald) are all asymptotically pivotal, and each can be modified to have an asymptotic standard F distribution or t distribution. We also suggest a finite sample variance correction further to improve the accuracy of the F or t approximation. Our proposed asymptotic F and t tests are very appealing to practitioners, as test statistics are simple modifications of the usual test statistics, and the F or t critical values are readily available from standard statistical tables. We also apply our methods to an empirical study on the causal effect of access to domestic and international markets on household consumption in rural China. The second paper "Should we go one step further? An Accurate Comparison of One-step and Two-step procedures in a Generalized Method of Moments Framework" (coauthored with Yixiao Sun) focuses on GMM procedure in time-series setting and provides an accurate comparison of one-step and two-step GMM procedures in a fixed-smoothing asymptotics framework. The theory developed in this paper shows that the two-step procedure outperforms the one-step method only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. We also provide clear guidance on how to choose a more efficient (or powerful) GMM estimator (or test) in practice. While our fixed smoothing asymptotic theory accurately describes sampling distribution of two-step GMM test statistic, the limiting distribution of conventional GMM statistics is non-standard, and its critical values need to be simulated or approximated by standard distributions in practice. In the last chapter, "Asymptotic F and t Tests in an Efficient GMM Setting" (coauthored with Yixiao Sun), we propose a simple and easy-to-implement modification to the trinity (QLM, LM, and Wald) of two-step GMM statistics and show that the modified test statistics are all asymptotically F distributed under the fixed-smoothing asymptotics. The modification is multiplicative and only involves the J statistic for testing over-identifying restrictions. In fact, what we propose can be regarded as the multiplicative variance correction for two-step GMM statistics that takes into account the additional asymptotic variance term under the fixed-smoothing asymptotics. The results in this paper can be immediately generalized to the GMM setting in the presence of clustered dependence.

Download or read book Robust Small Sample Accurate Inference in Moment Condition Models written by Ndame Lô and published by . This book was released on 2006 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Estimation and Inference for Generalized Linear Models written by Eva Cantoni and published by . This book was released on 1999 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inference in Generalized Linear Models with Applications written by Evan Byrne and published by . This book was released on 2019 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we first consider two problems involving the generalized linear model: sparse multinomial logistic regression (SMLR) and sketched clustering, which in the context of machine learning are forms of supervised and unsupervised learning, respectively. Conventional approaches to these problems fit the parameters of the model to the data by minimizing some regularized loss function between the model and data with an iterative gradient-based algorithm, which may suffer from various issues such as slow convergence or finding a sub-optimal solution. Slow convergence is particularly detrimental when applied to modern datasets, which may contain upwards of millions of sample points. We take an alternate inference approach based on approximate message passing, rather than optimization. In particular, we apply the hybrid generalized approximate message passing (HyGAMP) algorithm to both of these problems in order to learn the underlying parameters of interest. The HyGAMP algorithm approximates the sum-product or min-sum loopy belief propagation algorithms, which approximate minimum mean squared error (MMSE) or maximum a posteriori (MAP) estimation, respectively, of the unknown parameters of interest. We apply a simplified form of HyGAMP (SHyGAMP) to SMLR, where we show through numerical experiments that our approach meets or exceeds the performance of state-of-the-art SMLR algorithms with respect to classification accuracy and algorithm training time. We then apply the MMSE-SHyGAMP algorithm to the sketched clustering problem, where we also show through numerical experiments that our approach exceeds the performance of other state-of-the-art sketched clustering algorithms with respect to clustering accuracy and computational efficiency, as well as the widely used K-means++ algorithm in some regimes. Finally, we study the problem of adaptive detection from quantized measurements. We focus on the case of strong, but low-rank interference, which is motivated by wireless communications applications for the military, where the receiver is experiencing strong jamming from a small number of sources in a time-invariant channel. In this scenario, the receiver requires many antennas to effectively null out the interference, but at the cost of increased hardware complexity, and total volume of data to be processed. Using highly quantized measurements is one method of reducing the amount of data to be processed, but it is unknown how this affects detection performance. We first investigate the effect of quantized measurements on existing unquantized detection algorithms. We observe that unquantized detection algorithms applied to quantized measurements lack the ability to null arbitrarily large interference, despite being able to null arbitrarily large interference when applied to unquantized measurements. We then derive a generalized likelihood ratio test for the quantized measurement model, which gives rise to a generalized bilinear model. Via simulation, we empirically observe the quantized algorithm only offers a fraction of a decibel improvement in equivalent SNR relative to unquantized algorithms. We then evaluate alternative techniques to address the performance loss due to quantized measurements, including a novel analog pre-whitening using digitally controlled phase-shifters. In simulation, we observe that the new technique shows up to 8 dB improvement in equivalent SNR.

Download or read book Robust Estimation and Inference for Generalized Linear Models written by Eva Cantoni and published by . This book was released on 1999 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: