Optimal Smoothing in Single-Index Models

Härdle, Wolfgang Karl; Hall, Peter; Ichimura, Hidehiko

doi:10.1214/aos/1176349020

Cited by 632 publications

(495 citation statements)

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“…In the meantime, the condition that the initial estimate is √ N T -consistent is similar to the √ T -consistency condition in the one-index case (see Härdle, Hall andIchimura 1993 andCarroll et al 1997 for example). As a matter of the fact, this restriction is feasible as such an initial estimator can be obtained by using some existing methods (see, for example, Härdle and Stoker 1989;Horowitz and Härdle 1996).…”

Section: A4 the Bandwidth H Satisfiesmentioning

confidence: 90%

“…There is a growing interest in using single-index models in both the cross-sectional and time series cases (see, for example, Härdle, Hall and Ichimura 1993;Carroll et al 1997;Xia et al 2002;Yu and Ruppert 2002;Xia 2006;Gao 2007). So far as we know, however, there is little study in the theoretical and empirical analysis of singleindex models for panel data.…”

Section: For Examplementioning

confidence: 99%

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Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

Chen

Gao

2013

Econometric Reviews

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In this paper, we study semiparametric estimation for a single-index panel data model where the nonlinear link function varies among the individuals. We propose using the so-called refined minimum average variance estimation based on a local linear smoothing method to estimate both the parameters in the single-index and the average link function. As the cross-section dimension N and the time series dimension T tend to infinity simultaneously, we establish asymptotic distributions for the proposed parametric and nonparametric estimates. In addition, we provide two real-data examples to illustrate the finite sample behavior of the proposed estimation method in this paper.

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Section: A4 the Bandwidth H Satisfiesmentioning

confidence: 90%

Section: For Examplementioning

confidence: 99%

Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

Chen

Gao

2013

Econometric Reviews

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“…data has been extensively studied by many authors, to cite a few, Ichimura (1993) and Härdle, Hall and Ichimura (1993). In time series setting, (9) is a special case of the model studied by Xia, Tong and Li (1999).…”

Section: Semiparametric Extensionsmentioning

confidence: 99%

Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints

Lee

Ullah

2015

Journal of Business & Economic Statistics

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The equity premium, return on equity minus return on risk-free asset, is expected to be positive. We consider imposing such positivity constraint in local historical average (LHA) in nonparametric kernel regression framework. It is also extended to the semiparametric single index model when multiple predictors are used. We construct the constrained LHA estimator via an indicator function which operates as 'model-selection' between the unconstrained LHA and the bound of the constraint (zero for the positivity constraint). We smooth the indicator function by bagging (Breiman 1996a), which operates as 'model-averaging' and yields a combined forecast of unconstrained LHA forecasts and the bound of the constraint. The local combining weights are determined by the probability that the constraint is binding. Asymptotic properties of the constrained LHA estimators without and with bagging are established, which show how the positive constraint and bagging can help reduce the asymptotic variance and mean squared errors. Monte Carlo simulations are conducted to show the finite sample behavior of the asymptotic properties. In predicting U.S. equity premium, we show that substantial nonlinearity can be captured by LHA and that the local positivity constraint can improve out-of-sample prediction of the equity premium.

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“…See Powell, Stock and Stoker (1989), Ichimura and Lee (1991), Ichimura (1993), Härdle, Hall and Ichimura (1993), among many others for important results on the estimation and inference for this model when all the data are completely observed. We assume here that the response Y is missing at random.…”

Section: Single Index Regression Modelmentioning

confidence: 99%

Estimation in semiparametric models with missing data

Chen

Keilegom

2012

Ann Inst Stat Math

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This paper considers the problem of parameter estimation in a general class of semiparametric models when observations are subject to missingness at random. The semiparametric models allow for estimating functions that are non-smooth with respect to the parameter. We propose a nonparametric imputation method for the missing values, which then leads to imputed estimating equations for the finite dimensional parameter of interest. The asymptotic normality of the parameter estimator is proved in a general setting, and is investigated in detail for a number of specific semiparametric models. Finally, we study the small sample performance of the proposed estimator via simulations.

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Optimal Smoothing in Single-Index Models

Cited by 632 publications

References 0 publications

Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints

Estimation in semiparametric models with missing data

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