Showing papers by "Oliver Linton published in 2001"
TL;DR: In this paper, several kernel-based consistent tests of additivity in nonparametric regression have been developed for discrete covariates and parameters estimated from a semiparametric GMM criterion function.
81 citations
TL;DR: In this paper, the authors investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions and derive approximations to the first two moments of the estimator that are valid to second order.
Abstract: We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are valid to 'second order'. We use these approximations to define a method of bandwidth selection. We also propose a degrees of freedom like bias correction that improves the second order properties of the estimator but without requiring estimation of higher order derivatives of the unknown propensity score. We provide some numerical calibrations of the results.
75 citations
TL;DR: In this paper, the authors developed a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators, which is one practical definition of chaos.
Abstract: A positive Lyapunov exponent is one practical definition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the positive Lyapunov exponent is significantly rejected in many cases. One possible interpretation of this result is that the traditional exogenous models are better able to explain business cycle fluctuations than is the chaotic endogenous approach. However, our results are subject to a number of caveats, in particular our results could have been influenced by small sample bias, high noise level, incorrect filtering, and long memory of the data.
52 citations
TL;DR: In this paper, a nonparametric kernel smoothing method is proposed for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds, which is defined as the minimum of some localized population moment condition.
49 citations
TL;DR: In this paper, the authors proposed estimators of previous termfeatures of the distribution next term of an unobserved random variable W. They also provided estimators for quantiles and conditional on X moments of W under both nonparametric and semiparametric specifications.
47 citations
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TL;DR: New procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models using a full counting process framework that allows for left truncation and right censoring are proposed.
Abstract: We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring. Our procedures are based on kernels and on the idea of marginal integration. We provide a central limit theorem for our estimator.
37 citations
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TL;DR: In this article, the authors discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes, and point out the different implications of leading choices of bandwidths in numerator and denominator for the ability of the estimate to integrate to one and to have finite moments.
Abstract: We discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes. The kernel conditional density estimate is a ratio of joint and marginal density estimates. We point out the different implications of leading choices of bandwidths in numerator and denominator for the ability of the estimate to integrate to one and to have finite moments. Again bearing in mind different bandwidth possibilities, we discuss asymptotic theory for the estimate: asymptotic bias and variance are calculated under various conditions, an extended discussion of bandwidth choice is included, and a central limit theorem is given.
32 citations
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TL;DR: In this article, the authors proposed a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary NN, which is asymptotically equivalent to the infeasible local maximum likelihood estimator.
Abstract: We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum likelihood estimator [Staniswalis (1989)], and hence improves on standard kernel estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data.
24 citations
01 Jan 2001
TL;DR: In this paper, the authors propose three estimators of nonparametric regression functions subject to weak separability (WS) which have a limiting normal distribution and a convergence rate which is the same as that of an unconstrained nonparameterized estimator of a regression function of lower dimension.
Abstract: In this paper I propose three new estimators of nonparametric regression functions subject to weak separability (WS). The use of WS reduces the curse of dimensionality. WS nests other separability concepts such as (generalized) additive separability ((G)AS). The advantage of WS over (G)AS is that WS allows for interactions between regressors whereas (G)AS does not permit any interactions. The estimators use marginal integration and are shown to have a limiting normal distribution and a convergence rate which is the same as that of an unconstrained nonparametric estimator of a regression function of lower dimension. An attractive and unusual feature of two of my estimators is that regressors can have arbitrary convex support and that the integration regions can depend on the values of the remaining variables. The estimators can be iterated and I show that under strong assumptions further asymptotic efficiency improvements are possible. The computation of the estimators is simple. The performance of one of the estimators is studied in a simulation study.
23 citations
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TL;DR: In this paper, the authors discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes, and point out the different implications of leading choices of bandwidths in numerator and denominator for the ability of the estimate to integrate to one and to have finite moments.
Abstract: We discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes The kernel conditional density estimate is a ratio of joint and marginal density estimates We point out the different implications of leading choices of bandwidths in numerator and denominator for the ability of the estimate to integrate to one and to have finite moments Again bearing in mind different bandwidth possibilities, we discuss asymptotic theory for the estimate: asymptotic bias and variance are calculated under various conditions, an extended discussion of bandwidth choice is included, and a central limit theorem is given
21 citations
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TL;DR: In this article, a nonparametric estimator for the volatility structure of the zero coupon yield curve in the Heath, Jarrow-Morton framework is developed, incorporating cross-sectional restrictions along the maturity dimension, and also allowing for measurement errors, which arise from the estimation of the yield curve from noisy data.
Abstract: We develop a nonparametric estimator for the volatility structure of the zero coupon yield curve in the Heath, Jarrow-Morton framework. The estimator incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which arise from the estimation of the yield curve from noisy data. The estimates are implemented with daily CRSP bond data.
TL;DR: In this article, a nonparametric smoothing procedure is proposed for multivariate time series analysis based on the residuals from the Fair macromodel of the U.S. economy.
Abstract: We introduce a nonparametric smoothing procedure for nonparametric factor analysis of multivariate time series. Our main objective is to develop an adaptive method for estimating a time-varying covariance matrix. The asymptotic properties of the proposed procedures are derived. We present an application based on the residuals from the Fair macromodel of the U.S. economy. We find substantial evidence of time varying second moments and breaks in the contemporaneous correlation structure during the mid 1970's to the early 1980's.
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TL;DR: In this paper, the authors derived the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form and showed how the choice of smoothing parameters influences the estimator through higher order terms.
Abstract: We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both independent and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.
01 Jan 2001
TL;DR: In this paper, the authors derived the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form and showed how the choice of smoothing parameters influences the estimator through higher order terms.
Abstract: We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both independent and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.
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TL;DR: In this article, the authors propose estimators of features of the distribution of an unobserved random variable W. They use these features to evaluate the willingness of consumers to pay for a public good such as endangered species.
Abstract: We propose estimators of features of the distribution of an unobserved random variable W. What is observed is a sample of Y; V; X where a binary Y equals one when W exceeds a threshold V determined by experimental design, and X are covariates. Potential applications include bioassay and destructive duration analysis. Our empirical application is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values W (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers with characteristics X are asked whether they favor (with Y = 1 if yes and zero otherwise) a referendum that would provide the good at a cost V specified by experimental design. This paper provides estimators for quantiles and conditional on X moments of W under both nonparametric and semiparametric specifications.
TL;DR: In this article, the L q median of a sample of kernel estimators is used to estimate additive nonparametric regression models, and the convergence rate depends on the value of q.
Abstract: We propose a new method for estimating additive nonparametric regression models based on taking the L q median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q . For q > 3/2 one has the usual one-dimensional rate, but if q ≤ 3/2 the rate can be slower.
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TL;DR: In this article, the Linton-Mammen-Nielson-Tanggaard (LMSN) procedure was used as a proxy for the short-term U.S. interest rate.
Abstract: We show that the recently developed nonparametric procedure for fitting the term structure of interest rates developed by Linton, Mammen, Nielson and Tanggaard (2000) overall performs notably better than the highly flexible McCulloch (1975) cubic spline and Fama and Bliss (1987) bootstrap methods. However, if interest is limited to the Treasury bill region alone then the Fama-Bliss method demonstrates superior performance. We further show, via simulation, that using the estimated short rate from Linton-Mammen-Nielson-Tanggaard procedure as a proxy for the short rate has higher precision than the commonly used proxies of the one and three month Treasury bill rates. It is demonstrated that this precision is important when using proxies to estimate the stochastic process governing the evolution of the short rate.
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TL;DR: In this article, the authors investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions and derive approximations to the first two moments of the estimator that are valid to second order.
Abstract: We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are valid to 'second order'. We use these approximations to define a method of bandwidth selection. We also propose a degrees of freedom like bias correction that improves the second order properties of the estimator but without requiring estimation of higher order derivatives of the unknown propensity score. We provide some numerical calibrations of the results.
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TL;DR: In this article, the authors proposed a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary NN, which is asymptotically equivalent to the infeasible local maximum likelihood estimator.
Abstract: We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum likelihood estimator [Staniswalis (1989)], and hence improves on standard kernel estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data.
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TL;DR: In this paper, a new method for estimating additive nonparametric regression models based on taking the Lq median of a sample of kernel estimators is proposed, and the consistency and asymptotic normality of their procedures are established.
Abstract: We propose a new method for estimating additive nonparametric regression models based on taking the Lq median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q. For q > 3/2 one has the usual one-dimensional rate, but if q [less-than-or-equal] 3/2 the rate can be slower.
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TL;DR: In this paper, the authors propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models with a full counting process framework that allows for left truncation and right censoring.
Abstract: We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring. Our procedures are based on kernels and on the idea of marginal integration. we provide a central limit theorem for our estimator.
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TL;DR: In this article, a nonparametric estimator for the volatility structure of the zero coupon yield curve in the Heath-Jarrow-Morton framework is developed, which incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which arise from the estimation of the yield curve from noisy data.
Abstract: We develop a nonparametric estimator for the volatility structure of the zero coupon yield curve in the Heath-Jarrow-Morton framework. The estimator incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which arise from the estimation of the yield curve from noisy data. The estimates are implemented with daily CRSP bond data.
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TL;DR: In this paper, the authors investigate a class of estimators for linear regression models where the dependent variable is subject to bid-ask censoring, and propose an estimator based on a definition of error that is zero when the predictor lies between the actual bid price and ask price.
Abstract: We investigate a class of estimators for linear regression models where the dependent variable is subject to bid-ask censoring. Our estimation method is based on a definition of error that is zero when the predictor lies between the actual bid price and ask price, and linear outside this range. Our estimator minimizes a sum of such squared errors; it is nonlinear, and indeed the criterion function itself is non-smooth. We establish its asymptotic properties using the approach of Pakes and Pollard (1989). We compare the estimator with midpoint OLS. c 2001 Peking University Press