Download or read book Nonparametric Inference Based on Conditional Moment Inequalities written by Donald W. K. Andrews and published by . This book was released on 2013 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS's and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Download or read book Inference Based on Many Conditional Moment Inequalities written by Donald W. K. Andrews and published by . This book was released on 2015 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inference Based on Conditional Moment Inequalities written by Donald W. K. Andrews and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiscale Adaptive Inference on Conditional Moment Inequalities written by Timothy Armstrong and published by . This book was released on 2015 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple analytic formula, and to prove the asymptotic validity of a modified bootstrap procedure. The asymptotic distribution is extreme value, and the proof uses new techniques to overcome several technical obstacles. The test detects local alternatives that approach the identified set at the best rate among available tests in a broad class of models, and is adaptive to the smoothness properties of the data generating process. Our results also have implications for the use of moment selection procedures in this setting. We provide a monte carlo study and an empirical illustration to inference in a regression model with endogenously censored and missing data.
Download or read book Handbook of Econometrics written by and published by Elsevier. This book was released on 2020-11-25 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Econometrics, Volume 7A, examines recent advances in foundational issues and "hot" topics within econometrics, such as inference for moment inequalities and estimation of high dimensional models. With its world-class editors and contributors, it succeeds in unifying leading studies of economic models, mathematical statistics and economic data. Our flourishing ability to address empirical problems in economics by using economic theory and statistical methods has driven the field of econometrics to unimaginable places. By designing methods of inference from data based on models of human choice behavior and social interactions, econometricians have created new subfields now sufficiently mature to require sophisticated literature summaries. - Presents a broader and more comprehensive view of this expanding field than any other handbook - Emphasizes the connection between econometrics and economics - Highlights current topics for which no good summaries exist
Download or read book Handbook of Industrial Organization written by and published by Elsevier. This book was released on 2021-12-09 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Industrial Organization, Volume Four highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of expert authors. - Presents authoritative surveys and reviews of advances in theory and econometrics - Reviews recent research on capital raising methods and institutions - Includes discussions on developing countries
Download or read book Nonparametric Inference written by Z. Govindarajulu and published by World Scientific Publishing Company Incorporated. This book was released on 2007-01-01 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a solid foundation on nonparametric inference for students taking a graduate course in nonparametric statistics and serves as an easily accessible source for researchers in the area. With the exception of some sections requiring familiarity with measure theory, readers with an advanced calculus background will be comfortable with the material.
Download or read book Associated Sequences Demimartingales and Nonparametric Inference written by B.L.S. Prakasa Rao and published by Springer Science & Business Media. This book was released on 2011-11-04 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.
Download or read book Essays on Moment Inequalities written by Timothy Buck Armstrong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers inference in conditional moment inequality models. Chapter 1 derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. In contrast to other moment inequality settings, the rate of convergence is faster than root-n, and the asymptotic distribution depends entirely on nonbinding moments. The results require the development of new techniques that draw a connection between moment selection, irregular identification, bandwidth selection and nonstandard M-estimation. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A monte carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods. Chapter 2 proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting differs from those proposed in the literature in two important ways. First, confidence regions based on KS tests with the weighting function I propose converge to the identified set at a faster rate than existing procedures based on bounded weight functions in a broad class of models. This provides a theoretical justification for inverse variance weighting in this context, and contrasts with analogous results for conditional moment equalities in which optimal weighting only affects the asymptotic variance. Second, the new weighting changes the asymptotic behavior, including the rate of convergence, of the KS statistic itself, requiring a new asymptotic theory in choosing the critical value, which I provide. To make these comparisons, I derive rates of convergence for the confidence regions I propose along with new results for rates of convergence of existing estimators under a general set of conditions. A series of examples illustrates the broad applicability of the conditions. A monte carlo study examines the finite sample behavior of the confidence regions. Chapter 3 derives bounds in empirical models of first price auctions with unobserved heterogeneity. Many empirical studies of auctions rely on the assumption that the researcher observes all variables that make auctions differ ex ante. When there is unobserved heterogeneity, the direction of the bias this causes is known only in a few restrictive examples. In this chapter, I show that ignoring unobserved heterogeneity in a first price sealed bid auction with symmetric independent private values gives bounds on several quantities of economic interest under surprisingly general conditions. These include bidder profits (which can be used to recover bid preparation costs in entry models) and the efficiency loss of assigning the object randomly. I then turn to estimation of these bounds, and show that, when only the winning bid is available, the rate of convergence can be slower than the square root of the number of auctions observed and depends on the number of bidders. These results apply more generally to estimation of functionals of a distribution from repeated observations of an order statistic and may be of independent interest. I apply these methods to bound the efficiency loss from replacing a set of procurement auctions for highway construction in Michigan with random assignment.
Download or read book Econometric Analysis of Stochastic Dominance written by Yoon-Jae Whang and published by Cambridge University Press. This book was released on 2019-01-31 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive analysis of stochastic dominance through coverage of concepts, methods of estimation, inferential tools, and applications.
Download or read book Multivariate Robust Nonparametric Inference Based on Data Depth microform written by Shoja'eddin Chenouri and published by Library and Archives Canada = Bibliothèque et Archives Canada. This book was released on 2004 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Inferences on Conditional Quantile Processes written by Chuan Goh and published by . This book was released on 2007 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with tests of restrictions on the sample path of conditional quantile processes. These tests are tantamount to assessments of lack of fit for models of conditional quantile functions or more generally as tests of how certain covariates affect the distribution of an outcome variable of interest. This paper extends tests of the generalized likelihood ratio (GLR) type as introduced by Fan, Zhang and Zhang (2001) to nonparametric inference problems regarding conditional quantile processes. As such, the tests proposed here present viable alternatives to existing methods based on the Khmaladze (1981, 1988) martingale transformation. The range of inference problems that may be addressed by the methods proposed here is wide, and includes tests of nonparametric nulls against nonparametric alternatives as well as tests of parametric specifications against nonparametric alternatives. In particular, it is shown that a class of GLR statistics based on nonparametric additive quantile regressions have pivotal asymptotic distributions given by the suprema of squares of Bessel processes, as in Hawkins (1987) and Andrews (1993). The tests proposed here are also shown to be asymptotically rate-optimal for nonparametric hypothesis testing according to the formulations of Ingster (1993) and of Spokoiny (1996).
Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Download or read book Advances in Economics and Econometrics written by Econometric Society. World Congress and published by Cambridge University Press. This book was released on 2013-05-27 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume of edited papers from the Tenth World Congress of the Econometric Society 2010.
Download or read book Essays on Nonparametric Inference and Instrument Selection written by and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: My dissertation consists of two chapters on nonparametric inference and model selection in econometric models. First chapter constructs inference methods for nonparametric series regression models and introduces tests based on the infimum of t-statistics over different series terms. First, I provide a uniform asymptotic theory for the t-statistic process indexed by the number of series terms. Using this result, I show that the test based on the infimum of the t-statistics and its asymptotic critical value controls the asymptotic size with the undersmoothing condition. We can construct a valid confidence interval (CI) by test statistic inversion that has correct asymptotic coverage probability. Even when asymptotic bias terms are present without the undersmoothing condition, I show that the CI based on the infimum of the t-statistics bounds the coverage distortions. In an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002), proposed CI is close to or tighter than those based on existing methods with possibly ad hoc choice of series terms. Second chapter provides instrument selection criteria in instrumental variable (IV) regression model when there is a large set of instruments with potential invalidity. Economic data identified by IV model sometimes involve large sets of potential instruments and debates about their validity. Existing methods for instrument selection are largely based on a priori assumption of an instrument's validity and/or based on the first-order asymptotics, which may lead to a large finite sample bias with many and invalid instruments. First, I derive higher-order mean square error (MSE) approximation for two-stage least squares (2SLS), limited information maximum likelihood (LIML), modified Fuller (FULL) and bias-adjusted 2SLS (B2SLS) estimator allowing locally invalid instruments. Based on the approximation to the higher-order MSE, I propose an invalidity-robust instrument selection criteria (IRC) that capture two sources of finite sample bias at the same time: bias from using many instruments and bias from invalid instruments. I also show optimality result of choice of instruments based on the criteria of Donald and Newey (2001) under certain locally invalid instruments specification.
Download or read book New Methods for Econometric Inference written by Denis Nikolaevich Chetverikov and published by . This book was released on 2013 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical analysis. Chapter 1 develops a general nonparametric framework for testing monotonicity of a regression function. Using this framework, a broad class of new tests is introduced, which gives an empirical researcher a lot of flexibility to incorporate ex ante information she might have. Chapter 1 also develops new methods for simulating critical values, which are based on the combination of a bootstrap procedure and new selection algorithms. These methods yield tests that have correct asymptotic size and are asymptotically nonconservative. It is also shown how to obtain an adaptive rate optimal test that has the best attainable rate of uniform consistency against models whose regression function has Lipschitz-continuous first-order derivatives and that automatically adapts to the unknown smoothness of the regression function. Simulations show that the power of the new tests in many cases significantly exceeds that of some prior tests, e.g. that of Ghosal, Sen, and Van der Vaart (2000). An application of the developed procedures to the dataset of Ellison and Ellison (2011) shows that there is some evidence of strategic entry deterrence in pharmaceutical industry where incumbents may use strategic investment to prevent generic entries when their patents expire. Many economic models yield conditional moment inequalities that can be used for inference on parameters of these models. In chapter 2, I construct a new test of conditional moment inequalities based on studentized kernel estimates of moment functions. The test automatically adapts to the unknown smoothness of the moment functions, has uniformly correct asymptotic size, and is rate optimal against certain classes of alternatives. Some existing tests have nontrivial power against n-1/2 -local alternatives of a certain type whereas my method only allows for nontrivial testing against (n/ log n)-1/2-local alternatives of this type. There exist, however, large classes of sequences of well-behaved alternatives against which the test developed in this paper is consistent and those tests are not. In chapter 3 (coauthored with Victor Chernozhukov and Kengo Kato), we derive a central limit theorem for the maximum of a sum of high dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the Gaussian random vectors with the same covariance matrices as the original vectors. The key innovation of this result is that it applies even when the dimension of random vectors (p) is large compared to the sample size (n); in fact, p can be much larger than n. We also show that the distribution of the maximum of a sum of the random vectors with unknown covariance matrices can be consistently estimated by the distribution of the maximum of a sum of the conditional Gaussian random vectors obtained by multiplying the original vectors with i.i.d. Gaussian multipliers. This is the multiplier bootstrap procedure. Here too, p can be large or even much larger than n. These distributional approximations, either Gaussian or conditional Gaussian, yield a high-quality approximation to the distribution of the original maximum, often with approximation error decreasing polynomially in the sample size, and hence are of interest in many applications. We demonstrate how our central limit theorem and the multiplier bootstrap can be used for high dimensional estimation, multiple hypothesis testing, and adaptive specification testing. All these results contain non-asymptotic bounds on approximation errors.
Download or read book Nonparametric Inference for Extremal Conditional Quantiles written by Daisuke Kurisu and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
