Bootstrap-based Bandwidth Selection for Semiparametric Generalized Regression Estimators

This paper considers the problem of implementing semiparametric extremum estimators of a generalized regression model with an unknown link function. The class of estimator under consideration includes as special cases the semiparametric least-squares estimator of Ichimura (1993) as well as the semiparametric quasi-likelihood estimator of Klein and Spady (1993). In general, it is assumed to involve the computation of a nonparametric kernel estimate of the link function that appears in place of the true, but unknown, link function in the appropriate location in a smooth criterion function. The specific question considered in this paper concerns the practical selection of the degree of smoothing to be used in computing the nonparametric regression estimate. This paper proposes a method for selecting the smoothing parameter via resampling. The particular method suggested here involves using a resample of smaller size than the original sample. Specific guidance on selecting the resample size is given, and simulation evidence is presented to illustrate the utility of this method for samples of moderate size.Bandwidth selection, semiparametric, single-index model, bootstrap, m-out-of-n bootstrap, kernel smoothing

Nonparametric Inferences on Conditional Quantile Processes

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).quantile regression, nonparametric inference, minimax rate, additive models, local polynomials, generalized likelihood ratio

Nonstandard Estimation of Inverse Conditional Density-Weighted Expectations

This paper is concerned with the semiparametric estimation of function means that are scaled by an unknown conditional density function. Parameters of this form arise naturally in the consideration of models where interest is focused on the expected value of an integral of a conditional expectation with respect to a continuously distributed “special regressor”' with unbounded support. In particular, a consistent and asymptotically normal estimator of an inverse conditional density-weighted average is proposed whose validity does not require data-dependent trimming or the subjective choice of smoothing parameters. The asymptotic normality result is also rate adaptive in the sense that it allows for the formulation of the usual Wald-type inference procedures without knowledge of the estimator's actual rate of convergence, which depends in general on the tail behaviour of the conditional density weight. The theory developed in this paper exploits recent results of Goh & Knight (2009) concerning the behaviour of estimated regression-quantile residuals. Simulation experiments illustrating the applicability of the procedure proposed here to a semiparametric binary-choice model are suggestive of good small-sample performance.Semiparametric, identification at infinity, special regressor, rate-adaptive, regression quantile

Bandwidth Selection for Semiparametric Estimators Using the m-out-of-n Bootstrap

This paper considers a class of semiparametric estimators that take the form of density-weighted averages. These arise naturally in a consideration of semiparametric methods for the estimation of index and sample-selection models involving preliminary kernel density estimates. The question considered in this paper is that of selecting the degree of smoothing to be used in computing the preliminary density estimate. This paper proposes a bootstrap method for estimating the mean squared error and associated optimal bandwidth. The particular bootstrap method suggested here involves using a resample of smaller size than the original sample. This method of bandwidth selection is presented with specific reference to the case of estimators of average densities, of density-weighted average derivatives and of density-weighted conditional covariances.bandwidth selection, density-weighted averages, bootstrap, m-out-of-n bootstrap, kernel density estimation

Efficient Semiparametric Detection of Changes in Trend

This paper proposes a test for the correct specification of a dynamic time-series model that is taken to be stationary about a deterministic linear trend function with no more than a finite number of discontinuities in the vector of trend coefficients. The test avoids the consideration of explicit alternatives to the null of trend stability. The proposal also does not involve the detailed modelling of the data-generating process of the stochastic component, which is simply assumed to satisfy a certain strong invariance principle for stationary causal processes taking a general form. As such, the resulting inference procedure is effectively an omnibus specification test for segmented linear trend stationarity. The test is of Wald-type, and is based on an asymptotically linear estimator of the vector of total-variation norms of the trend parameters whose influence function coincides with the efficient influence function. Simulations illustrate the utility of this procedure to detect discrete breaks or continuous variation in the trend parameter as well as alternatives where the trend coefficients change randomly each period. This paper also includes an application examining the adequacy of a linear trend-stationary specification with infrequent trend breaks for the historical evolution of U.S. real output.Structural change, trend-stationary processes, nonparametric regression, efficient influence function

Specification analysis of linear quantile models

This paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels. These tests may be applied to assess the validity of post-estimation inferences regarding the effect of conditioning variables on the distribution of outcomes. We show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure. Monte Carlo evidence and an application to the empirical analysis of age-earnings curves are included.Escanciano acknowledges the support of the Spanish Plan Nacional de I+D+I, reference number SEJ2007-62908

Structure and properties of lead zirconate titanate thin films by pulsed laser deposition

Ph.DDOCTOR OF PHILOSOPH

Stated Choice Analysis of Conditional Purchase and Information Cue Effects in Online Group Purchase

Group-purchase institutions, a type of Internet shopping website, allows consumers to aggregate their demands for a product to gain discounts in purchase price. Modeling consumers’ bidding behavior in this institution using the economic perspective of constraint, expectation, and preference interactions, we study two group-purchase mechanisms (i.e., conditional purchase and information cue) on a buyer’s purchase choice across competing group-purchase alternatives. Using a conditional purchase mechanism, a buyer is not obliged to commit to the purchase if the best price is not met (i.e., the final offered price is greater than the best available lowest price). Through the information cue, a buyer could obtain information on the current number of orders collected. We analyzed a set of laboratory experimental data based on a group-purchase institution using the stated choice method. We find that a buyer is more likely to buy through group-purchase when a conditional purchase mechanism is provided. However, providing more information does not necessarily alleviate buyer uncertainty and inertia. The presence of information cue does induce them to choose a riskier but cheaper group-purchase option. In such cases, the choice elasticity of a risky group-purchase option is more sensitive to the information cue than to the conditional purchase mechanism

Intent-driven approach to innovations

Master'sMASTER OF ARTS (INDUSTRIAL DESIGN