Download or read book Efficient Estimation in a Generalized Regression Model written by Oscar Tin Go and published by . This book was released on 1989 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Use of Submodels as a Basis for Efficient Estimation of Complex Models written by Abdollah Safari and published by . This book was released on 2017 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider problems where the true underlying models are complex and obtaining the maximum likelihood estimator (MLE) of the true model is challenging or time-consuming. In our first paper, we investigate a general class of parameter-driven models for time series of counts. Depending on the distribution of the latent variables, these models can be highly complex. We consider a set of simple models within this class as a basis for estimating the regression coefficients in the more complex models. We also derive standard errors (SEs) for these new estimators. We conduct a comprehensive simulation study to evaluate the accuracy and efficiency of our estimators and their SEs. Our results show that, except in extreme cases, the maximizer of the Poisson generalized linear model (the simplest estimator in our context) is an efficient, consistent, and robust estimator with a well-behaved standard error. In our second paper, we work in the context of display advertising, where the goal is to estimate the probability of conversion (a pre-defined action such as making a purchase) after a user clicks on an ad. In addition to accuracy, in this context, the speed with which the estimate can be computed is critical. Again, computing the MLEs of the true model for the observed conversion statuses (which depends on the distribution of the delays in observing conversions) is challenging, in this case because of the huge size of the data set. We use a logistic regression model as a basis for estimation, and then adjust this estimate for its bias. We show that our estimation algorithm leads to accurate estimators and requires far less computation time than does the MLE of the true model. Our third paper also concerns the conversion probability estimation problem in display advertising. We consider a more complicated setting where users may visit an ad multiple times prior to taking the desired action (e.g., making a purchase). We extend the estimator that we developed in our second paper to incorporate information from such visits. We show that this new estimator, the DV-estimator (which accounts for the distributions of both the conversion delay times and the inter-visit times) is more accurate and leads to better confidence intervals than the estimator that accounts only for delay times (the D-estimator). In addition, the time required to compute the DV-estimate for a given data set is only moderately greater than that required to compute the D-estimate -- and is substantially less than that required to compute the MLE. In summary, in a variety of settings, we show that estimators based on simple, misspecified models can lead us to accurate, precise, and computationally efficient estimates of both the key model parameters and their standard deviations.

Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

Download or read book Efficient Estimation in the Generalized Semilinear Model written by Mary Jane Emond and published by . This book was released on 1993 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Estimation in a Regression Model with Missing Responses written by Scott Daniel Crawford and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article examines methods to efficiently estimate the mean response in a linear model with an unknown error distribution under the assumption that the responses are missing at random. We show how the asymptotic variance is affected by the estimator of the regression parameter and by the imputation method. To estimate the regression parameter the Ordinary Least Squares method is efficient only if the error distribution happens to be normal. If the errors are not normal, then we propose a One Step Improvement estimator or a Maximum Empirical Likelihood estimator to estimate the parameter efficiently. In order to investigate the impact that imputation has on estimation of the mean response, we compare the Listwise Deletion method and the Propensity Score method (which do not use imputation at all), and two imputation methods. We show that Listwise Deletion and the Propensity Score method are inefficient. Partial Imputation, where only the missing responses are imputed, is compared to Full Imputation, where both missing and non-missing responses are imputed. Our results show that in general Full Imputation is better than Partial Imputation. However, when the regression parameter is estimated very poorly, then Partial Imputation will outperform Full Imputation. The efficient estimator for the mean response is the Full Imputation estimator that uses an efficient estimator of the parameter.

Download or read book Semiparametrically Efficient Estimation of the Average Linear Regression Function written by Bryan S. Graham and published by . This book was released on 2018 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: ELet Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment control variables. Here X may include (combinations of) continuous, discrete, and/or non-mutually exclusive "treatments". Consider the linear regression of Y onto X in a subpopulation homogenous in W = w (formally a conditional linear predictor). Let b0 (w) be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average b0 = E[b0 (W)]. When X is binary-valued (multi-valued) our procedure recovers the (a vector of) average treatment effect(s). When X is continuously-valued, or consists of multiple non-exclusive treatments, our estimand coincides with the average partial effect (APE) of X on Y when the underlying potential response function is linear in X, but otherwise heterogenous across agents. When the potential response function takes a general nonlinear/heterogenous form, and X is continuously-valued, our procedure recovers a weighted average of the gradient of this response across individuals and values of X. We provide a simple, and semiparametrically efficient, method of covariate adjustment for settings with complicated treatment regimes. Our method generalizes familiar methods of covariate adjustment used for program evaluation as well as methods of semiparametric regression (e.g., the partially linear regression model).

Download or read book Generalized Linear Models written by P. McCullagh and published by Routledge. This book was released on 2019-01-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and ot

Download or read book Efficient Estimation of Regression Models with User specified Parametric Model for Heteroskedasticty written by Saraswata Chaudhuri and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Estimation with Missing Values in Cross Section and Panel Data written by Bhavna Rai and published by . This book was released on 2021 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1: Efficient Estimation with Missing Data and EndogeneityI study the problem of missing values in both the outcome and the covariates in linear models with endogenous covariates. I propose an estimator that improves efficiency relative to a Two Stage Least Squares (2SLS) based only on the complete cases. My framework also unifies the literature on missing data and combining data sets, and includes the "Two-Sample 2SLS" as a special case. The method is an extension of Abrevaya and Donald (2017), who provide methods of improving efficiency over complete cases estimators in linear models with cross-section data and missing covariates. I also provide guidance on dealing with missing values in the instruments and in commonly used nonlinear functions of the endogenous covariates, likes squares and interactions, without introducing inconsistency in the estimates.Chapter 2: Imputing Missing Covariate Values in Nonlinear ModelsI study the problem of missing covariate values in nonlinear models with continuous or discrete covariates. In order to use the information in the incomplete cases, I propose an inverse probability weighted one-step imputation estimator that provides gains in efficiency relative to the complete cases estimator using a reduced form for the outcome in terms of the always-observed covariates. Unlike the two-step imputation and dummy variable methods commonly used in empirical work ,my estimator is consistent for a wide class of nonlinear models. It relies only on the commonly used "missing at random" assumption, and provides a specification test for the resulting restrictions. I show how the results apply to nonlinear models for fractional and nonnegative responses.Chapter 3: Efficient Estimation of Linear Panel Data Models with Missing CovariatesWe study the problem of missing covariates in the context of linear, unobserved effects panel data models. In order to use information on incomplete cases, we propose generalized method of moments (GMM) estimation. By using information on the incomplete cases from all time periods, the proposed estimators provide gains in efficiency relative to the fixed effects (and Mundlak) estimator that use only the complete cases. The method is an extension of Abrevaya and Donald(2017), who consider a linear model with cross-sectional data and incorporate the linear imputation method in the set of moment conditions to obtain gains in efficiency. Our first proposed estimator uses the assumption of strict exogeneity of the covariates as well as the selection, while allowing the selection to be correlated with the observed covariates and unobserved heterogeneity in both the outcome equation and the imputation equation. We also consider the case in which the covariates are only sequentially exogenous and propose an estimator based on the method of forward orthogonal deviations introduced by Arellano and Bover (1995). Our framework suggests a simple test for whether selection is correlated with unobserved shocks, both contemporaneous and those in other time periods.

Download or read book Efficient Inference in General Semiparametric Regression Models written by Arnab Maity and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiparametric regression has become very popular in the field of Statistics over the years. While on one hand more and more sophisticated models are being developed, on the other hand the resulting theory and estimation process has become more and more involved. The main problems that are addressed in this work are related to efficient inferential procedures in general semiparametric regression problems. We first discuss efficient estimation of population-level summaries in general semiparametric regression models. Here our focus is on estimating general population-level quantities that combine the parametric and nonparametric parts of the model (e.g., population mean, probabilities, etc.). We place this problem in a general context, provide a general kernel-based methodology, and derive the asymptotic distributions of estimates of these population-level quantities, showing that in many cases the estimates are semiparametric efficient. Next, motivated from the problem of testing for genetic effects on complex traits in the presence of gene-environment interaction, we consider developing score test in general semiparametric regression problems that involves Tukey style 1 d.f form of interaction between parametrically and non-parametrically modeled covariates. We develop adjusted score statistics which are unbiased and asymptotically efficient and can be performed using standard bandwidth selection methods. In addition, to over come the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented using standard computational methods. Finally, we take up the important problem of estimation in a general semiparametric regression model when covariates are measured with an additive measurement error structure having normally distributed measurement errors. In contrast to methods that require solving integral equation of dimension the size of the covariate measured with error, we propose methodology based on Monte Carlo corrected scores to estimate the model components and investigate the asymptotic behavior of the estimates. For each of the problems, we present simulation studies to observe the performance of the proposed inferential procedures. In addition, we apply our proposed methodology to analyze nontrivial real life data sets and present the results.

Download or read book Methods for Estimation and Inference in Modern Econometrics written by Stanislav Anatolyev and published by CRC Press. This book was released on 2011-06-07 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers important topics in econometrics. It discusses methods for efficient estimation in models defined by unconditional and conditional moment restrictions, inference in misspecified models, generalized empirical likelihood estimators, and alternative asymptotic approximations. The first chapter provides a general overview of established nonparametric and parametric approaches to estimation and conventional frameworks for statistical inference. The next several chapters focus on the estimation of models based on moment restrictions implied by economic theory. The final chapters cover nonconventional asymptotic tools that lead to improved finite-sample inference.

Download or read book Frontiers In Statistics written by Jianqing Fan and published by World Scientific. This book was released on 2006-07-17 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades, many areas of statistical inference have experienced phenomenal growth. This book presents a timely analysis and overview of some of these new developments and a contemporary outlook on the various frontiers of statistics.Eminent leaders in the field have contributed 16 review articles and 6 research articles covering areas including semi-parametric models, data analytical nonparametric methods, statistical learning, network tomography, longitudinal data analysis, financial econometrics, time series, bootstrap and other re-sampling methodologies, statistical computing, generalized nonlinear regression and mixed effects models, martingale transform tests for model diagnostics, robust multivariate analysis, single index models and wavelets.This volume is dedicated to Prof. Peter J Bickel in honor of his 65th birthday. The first article of this volume summarizes some of Prof. Bickel's distinguished contributions.

Download or read book Relative Error Estimation and Efficient Estimation of Censored Linear Regression Model written by Yuanyuan Lin and published by . This book was released on 2011 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of Generalized Regression Models by the Grouping Method written by Kazumitsu Nawata and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Efficient and Robust Estimation in Semiparametric Linear Regression Models with Missing Data written by Alex Catane Bajamonde and published by . This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions written by Whitney K. Newey and published by . This book was released on 1987 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modern Methods for Robust Regression written by Robert Andersen and published by SAGE. This book was released on 2008 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering an in-depth treatment of robust and resistant regression, this volume takes an applied approach and offers readers empirical examples to illustrate key concepts.