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21
Large Sample Sieve Estimation of SemiNonparametric Models
 Handbook of Econometrics
, 2007
"... Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method o ..."
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Cited by 92 (17 self)
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Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in seminonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. This chapter describes estimation of seminonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve Mestimates, pointwise normality of series estimates of regression functions, rootn asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.
Economic Choices
 American Economic Review
, 2001
"... ome detail more recent developments in the economic theory of choice, and modifications to this theory that are being forced by experimental evidence from cognitive psychology. I will close with a survey of statistical methods that have developed as part of the research program on economic choice be ..."
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Cited by 55 (2 self)
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ome detail more recent developments in the economic theory of choice, and modifications to this theory that are being forced by experimental evidence from cognitive psychology. I will close with a survey of statistical methods that have developed as part of the research program on economic choice behavior. Science is a cooperative enterprise, and my work on choice behavior reflects not only my own ideas, but the results of exchange and collaboration with many other scholars. 1 First, of course, is my colaureate James Heckman, who among his many contributions pioneered the important area of dynamic discrete choice analysis. Nine other individuals who played a major role in channeling microeconometrics and choice theory toward their modern forms, and had a particularly important influence on my own work, are Zvi Griliches, L.L. Thurstone, Jacob Marschak, Duncan Luce, Danny Kahneman, Amos Tversky, Moshe BenAkiva, Charles Manski, and Kenneth Train. A gallery of their p
Approximation theory of the MLP model in neural networks
 ACTA NUMERICA
, 1999
"... In this survey we discuss various approximationtheoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. Mathematically it is one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are appr ..."
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Cited by 39 (3 self)
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In this survey we discuss various approximationtheoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. Mathematically it is one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are approximationtheoretic in character. Most of the research we will discuss is of very recent vintage. We will report on what has been done and on various unanswered questions. We will not be presenting practical (algorithmic) methods. We will, however, be exploring the capabilities and limitations of this model. In the first
Land of Addicts? An Empirical Investigation of HabitBased Asset Pricing Models
, 2003
"... A leading explanation of aggregate stock market behavior suggests that assets are priced as if there were a representative investor whose utility is a power function of the difference between aggregate consumption and a “habit" level, where the habit is some function of lagged and (possibly) contemp ..."
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Cited by 33 (3 self)
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A leading explanation of aggregate stock market behavior suggests that assets are priced as if there were a representative investor whose utility is a power function of the difference between aggregate consumption and a “habit" level, where the habit is some function of lagged and (possibly) contemporaneous consumption. But theory does not provide precise guidelines about the parametric functional relationship between the habit and aggregate consumption. This makes formal estimation and testing challenging; at the same time, it raises an empirical question about the functional form of the habit that best explains asset pricing data. This paper studies the ability of a general class of habitbased asset pricing models to match the conditional moment restrictions implied by asset pricing theory. Our approach is to treat the functional form of the habit as unknown, and to estimate it along with the rest
Semiparametric ARX Neural Network Models with an Application to Forecasting Inflation
, 2001
"... In this paper we examine semiparametric nonlinear autoregressive models with exogenous variables (NLARX) via three classes of artificial neural networks: the first one uses smooth sigmoid activation functions; the second one uses radial basis activation functions; and the third one uses ridgelet act ..."
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Cited by 10 (1 self)
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In this paper we examine semiparametric nonlinear autoregressive models with exogenous variables (NLARX) via three classes of artificial neural networks: the first one uses smooth sigmoid activation functions; the second one uses radial basis activation functions; and the third one uses ridgelet activation functions. We provide root mean squared error convergence rates for these ANN estimators of the conditional mean and median functions with stationary betamixing data. As an empirical application, we compare the forecasting performance of linear and semiparametric NLARX models of U.S. inflation. We find that all of our semiparametric models outperform a benchmark linear model based on various forecast performance measures. In addition, a semiparametric ridgelet NLARX model which includes various lags of historical inflation and the GDP gap is best in terms of both forecast mean squared error and forecast mean absolute deviation error.
Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
, 2000
"... This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the est ..."
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Cited by 8 (2 self)
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This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1 % level with an exception in some higher power transformed absolute returns.
Time series estimation of the effects of natural experiments
 Journal of Econometrics
, 2006
"... Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We d ..."
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Cited by 7 (6 self)
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Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We draw on the extensive literature of
Statistical Inference, The Bootstrap, And Neural Network Modeling With Application To Foreign Exchange Rates
 IEEE TRANS. ON NEURAL NETWORKS
, 2000
"... In this paper we propose tests for individual and joint irrelevance of network inputs. Such tests can be used to determine whether an input or group of inputs "belong" in a particular model, thus permitting valid statistical inference based on estimated feedforward neural network models. The approac ..."
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Cited by 6 (0 self)
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In this paper we propose tests for individual and joint irrelevance of network inputs. Such tests can be used to determine whether an input or group of inputs "belong" in a particular model, thus permitting valid statistical inference based on estimated feedforward neural network models. The approaches employ well known statistical resampling techniques. We conduct a small Monte Carlo Experiment showing that our tests have reasonable level and power behavior, and we apply our methods to examine whether there are predictable regularities in foreign exchange rates. We nd that exchange rates do appear to contain information that is exploitable for enhanced point prediction, but the nature of the predictive relations evolves through time.
Parametric and Nonparametric Estimation of CovariateConditioned Average Effects
 UCSD DEPT. OF ECONOMICS DISCUSSION PAPER
, 2005
"... This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approac ..."
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Cited by 4 (4 self)
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This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification and estimation of causal effects without requiring exogenous instruments, generalizing the classical structural equations approach; it relaxes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates; and it accommodates mutual causality, generalizing the DAG approach. We provide necessary and sufficient conditions for identification of covariateconditioned average causal effects, parametric and nonparametric estimation results, and new tests for unconfoundedness.