19,149 research outputs found
Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates
We study semiparametric varying-coefficient partially linear models when some
linear covariates are not observed, but ancillary variables are available.
Semiparametric profile least-square based estimation procedures are developed
for parametric and nonparametric components after we calibrate the error-prone
covariates. Asymptotic properties of the proposed estimators are established.
We also propose the profile least-square based ratio test and Wald test to
identify significant parametric and nonparametric components. To improve
accuracy of the proposed tests for small or moderate sample sizes, a wild
bootstrap version is also proposed to calculate the critical values. Intensive
simulation experiments are conducted to illustrate the proposed approaches.Comment: Published in at http://dx.doi.org/10.1214/07-AOS561 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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A multifactor consumption based asset pricing model of the UK stock market: The US stock market as a wealth reference
Here a multifactor model of UK stock returns is developed, replacing the conventional consumption habit reference by a relation that depends on US wealth. Two step Instrumental Variables and Generalized Method of Moments estimators are applied to reduce the impact of weak instruments. The standard errors are corrected for the generated regressor problem and the model is found to explain UK excess returns by UK consumption growth and expected US excess returns. Hence, controlling for nomina l effects by subtracting a risk free rate and conditioning on real US excess returns provides a coherent explanation of the equity premium puzzle
Partially linear additive quantile regression in ultra-high dimension
We consider a flexible semiparametric quantile regression model for analyzing
high dimensional heterogeneous data. This model has several appealing features:
(1) By considering different conditional quantiles, we may obtain a more
complete picture of the conditional distribution of a response variable given
high dimensional covariates. (2) The sparsity level is allowed to be different
at different quantile levels. (3) The partially linear additive structure
accommodates nonlinearity and circumvents the curse of dimensionality. (4) It
is naturally robust to heavy-tailed distributions. In this paper, we
approximate the nonlinear components using B-spline basis functions. We first
study estimation under this model when the nonzero components are known in
advance and the number of covariates in the linear part diverges. We then
investigate a nonconvex penalized estimator for simultaneous variable selection
and estimation. We derive its oracle property for a general class of nonconvex
penalty functions in the presence of ultra-high dimensional covariates under
relaxed conditions. To tackle the challenges of nonsmooth loss function,
nonconvex penalty function and the presence of nonlinear components, we combine
a recently developed convex-differencing method with modern empirical process
techniques. Monte Carlo simulations and an application to a microarray study
demonstrate the effectiveness of the proposed method. We also discuss how the
method for a single quantile of interest can be extended to simultaneous
variable selection and estimation at multiple quantiles.Comment: Published at http://dx.doi.org/10.1214/15-AOS1367 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Asset Pricing Theories, Models, and Tests
An important but still partially unanswered question in the investment field is why different assets earn substantially different returns on average. Financial economists have typically addressed this question in the context of theoretically or empirically motivated asset pricing models. Since many of the proposed “risk” theories are plausible, a common practice in the literature is to take the models to the data and perform “horse races” among competing asset pricing specifications. A “good” asset pricing model should produce small pricing (expected return) errors on a set of test assets and should deliver reasonable estimates of the underlying market and economic risk premia. This chapter provides an up-to-date review of the statistical methods that are typically used to estimate, evaluate, and compare competing asset pricing models. The analysis also highlights several pitfalls in the current econometric practice and offers suggestions for improving empirical tests
Semiparametric Bayesian inference in smooth coefficient models
We describe procedures for Bayesian estimation and testing in cross-sectional, panel data and nonlinear smooth coefficient models. The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - for example, estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model. We apply our methods using data from the National Longitudinal Survey of Youth (NLSY). Using the NLSY data we first explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. We also examine a model of female labor supply and use this example to illustrate how the described techniques can been applied in nonlinear settings
Inference of time-varying regression models
We consider parameter estimation, hypothesis testing and variable selection
for partially time-varying coefficient models. Our asymptotic theory has the
useful feature that it can allow dependent, nonstationary error and covariate
processes. With a two-stage method, the parametric component can be estimated
with a -convergence rate. A simulation-assisted hypothesis testing
procedure is proposed for testing significance and parameter constancy. We
further propose an information criterion that can consistently select the true
set of significant predictors. Our method is applied to autoregressive models
with time-varying coefficients. Simulation results and a real data application
are provided.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1010 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Variable selection in measurement error models
Measurement error data or errors-in-variable data have been collected in many
studies. Natural criterion functions are often unavailable for general
functional measurement error models due to the lack of information on the
distribution of the unobservable covariates. Typically, the parameter
estimation is via solving estimating equations. In addition, the construction
of such estimating equations routinely requires solving integral equations,
hence the computation is often much more intensive compared with ordinary
regression models. Because of these difficulties, traditional best subset
variable selection procedures are not applicable, and in the measurement error
model context, variable selection remains an unsolved issue. In this paper, we
develop a framework for variable selection in measurement error models via
penalized estimating equations. We first propose a class of selection
procedures for general parametric measurement error models and for general
semi-parametric measurement error models, and study the asymptotic properties
of the proposed procedures. Then, under certain regularity conditions and with
a properly chosen regularization parameter, we demonstrate that the proposed
procedure performs as well as an oracle procedure. We assess the finite sample
performance via Monte Carlo simulation studies and illustrate the proposed
methodology through the empirical analysis of a familiar data set.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ205 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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