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This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If estimation

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM. This variance estimator enables cluster-robust inference when there is two-way or multi-way clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can overreject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited differences-in-differences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0.05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a wild cluster bootstrap performs better.

We study the effect of the level of inequality in society on individual well-being using a total of 123,668 answers to a survey question about ‘‘happiness’’. We find that individuals have a lower tendency to report themselves happy when inequality is high, even after controlling for individual income, a large set of personal characteristics, and year and country (or, in the case of the US, state) dummies. The effect, however, is more precisely defined statistically in Europe than in the US. In addition, we find striking differences across groups. In Europe, the poor and those on the left of the political spectrum are unhappy about inequality; whereas in the US the happiness of the poor and of those on the left is uncorrelated with inequality. Interestingly, in the US, the rich are bothered by inequality. Comparing across continents, we find that left-wingers in Europe are more hurt by inequality than left-wingers in the US. And the poor in Europe are more concerned with inequality than the poor in America, an effect that is large in terms of size but is only significant at the 10% level. We argue that these findings are consistent with the perception (not necessarily the reality) that Americans have been living in a mobile society, where individual effort can move people up and down the income ladder, while Europeans believe that they live in less mobile societies.

this paper, we propose generalized additive mixed models (GAMMs), which are an additive extension of generalized linear mixed models in the spirit of Hastie and Tibshirani (1990). This new class of models uses additive nonparametric functions to model covariate effects while accounting for overdispersion and correlation by adding random effects to the additive predictor. GAMMs encompass nested and crossed designs and are applicable to clustered, hierarchical and spatial data. We estimate the nonparametric functions using smoothing splines, and jointly estimate the smoothing parameters and the variance components using marginal quasi-likelihood. This marginal quasilikelihood approach is an extension of the restricted maximum likelihood approach used by Wahba (1985) and Kohn, et al. (1991) in the classical nonparametric regression model (Kohn, et al. 1991, eq 2.1), and by Zhang, et al. (1998) in Gaussian nonparametric mixed models, where they treated the smoothing parameter as an extra variance component. In view of numerical integration often required by maximizing the objective functions, double penalized quasi-likelihood (DPQL) is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the proposed method is that it allows us to make systematic inference on all model components of GAMMs within a unified parametric mixed model framework. Specifically, our estimation of the nonparametric functions, the smoothing parameters and the variance components in GAMMs can proceed by fitting a working GLMM using existing statistical software, which iteratively fits a linear mixed model to a modified dependent variable. When the data are sparse (e.g., binary), the DPQL estimators of the variance components are found to be subject t...

Introduction Estimating functions provide a general framework for finding estimators and studying their properties in many di#erent kinds of statistical models, including stochastic process models. An estimating function is a function of the data as well as of the parameter to be estimated. An estimator is obtained by equating the estimating function to zero and solving the resulting estimating equation with respect to the parameter. The idea of using estimating equations is an old one and goes back at least to Karl Pearson's introduction of the method of moments. The term estimating function may have been coined by Kimball (1946). The estimating function approach has turned out to be very useful in obtaining, improving and studying estimators for discretely sampled parametric di#usion-type models, where the likelihood function is usually not explicitly known. Estimating functions are often constructed by combining relationships (dependent on the unknown parameter) between an observa

The results of this study provide insight into why some universities generate more new companies to exploit their intellectual property than do others. We compare four different explanations for cross-institutional variation in new firm formation rates from university technology licensing offices (TLOs) over the 1994-1998 period – the availability of venture capital in the university area; the commercial orientation of university research and development; intellectual eminence; and university policies. The results show that intellectual eminence, and the policies of making equity investments in TLO start-ups and maintaining a low inventor’s share of royalties increase new firm formation. The paper discusses the implications of these results for university and public policy. 2 I.

this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.

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