Testing in semiparametric models with interaction, with applications to gene–environment interactions

Summary.  Motivated from the problem of testing for genetic effects on complex traits in the presence of gene–environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 degree-of-freedom form of interaction between parametrically and non-parametrically modelled covariates. We find that the score test in this type of model, as recently developed by Chatterjee and co-workers in the fully parametric setting, is biased and requires undersmoothing to be valid in the presence of non-parametric components. Moreover, in the presence of repeated outcomes, the asymptotic distribution of the score test depends on the estimation of functions which are defined as solutions of integral equations, making implementation difficult and computationally taxing. We develop profiled score statistics which are unbiased and asymptotically efficient and can be performed by using standard bandwidth selection methods. In addition, to overcome the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented by using standard computational methods. We present simulation studies to evaluate type I error and power of the method proposed compared with a naive test that does not consider interaction. Finally, we illustrate our methodology by analysing data from a case–control study of colorectal adenoma that was designed to investigate the association between colorectal adenoma and the candidate gene NAT2 in relation to smoking history.     

The illusion of independence: Spun-off firms’ risk-taking as a function of status and attachment to the parent firm

This paper examines the post-divestiture behavior of spun-off firms. Drawing on the spin-off literature and middle-status conformity theory, we argue that spun-off firms—as newly independent and publicly traded firms—tend to limit their risk-taking behavior to match the expectations of a crucial audience, i.e., security analysts. Following the logic of middle-status conformity theory, we hypothesize that firms with mid-level status are particularly susceptible to analysts' pressures, whereas high- and low-status firms are free to take greater risks. Crucially, however, we propose that this relationship is less pronounced for spun-off firms that are more attached to their parent firms, as formal and informal linkages between these two types of firms can endure beyond the separation and limit spun-off firms' independence. Using a dataset of 102 spin-off transactions occurring between 1995 and 2010, we find empirical support for a U-shaped relationship between spun-off firms' status and risk-taking. This relationship is attenuated when spun-off firms are more attached to their parents. We contribute to the spin-off literature by demonstrating that a spun-off firm's post-divestiture behavior is determined by the capital market audience's expectations and the attachment to the parent firm. In so doing, we also contribute to the literature on middle-status conformity theory by identifying a boundary condition of the theory. Additionally, we make a methodological contribution by combining ideas from the spin-off and institutional theory literature to develop a particularly comprehensive measure of attachment.     

A bootstrap test for single index models

Single index models are frequently used in econometrics and biometrics. Logit and Probit models arc special cases with fixed link functions. In this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to rind a more accurate distribution under the null than the normal approximation. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has a more accurate level than the normal approximation.     

Nonparametric estimation of noisy integral equations of the second kind

In this overview we will show that many statistical estimation problems can be considered as empirical solutions of noisy integral equations of the second kind. We illustrate this by giving a series of examples and we will discuss a general nonparametric approach based on plugging-in nonparametric estimates of the integral kernel and of the intercept of the integral equation.     

Judgmental Forecasting: Cognitive Reflection and Decision Speed

This research analyzes how individual differences affect performance in judgmental time‐series forecasting. Decision makers with the ability to balance intuitive judgment with cognitive deliberation, as measured by the cognitive reflection test, tend to have lower forecast errors. This relationship holds when controlling for intelligence. Furthermore, forecast errors increase for very fast or very slow decisions. We provide evidence that forecast performance can be improved by manipulating decision speed.     

Gaining Access to Economically Marginalized Rural Populations: Lessons Learned from Nonprobability Sampling*

Poverty is a significant problem in rural America. Gaining access to economically marginalized rural populations in order to recruit individuals to participate in a research study, however, is often a challenge. This article compares three different nonprobability sampling techniques that have been used to recruit rural, low-income mothers—purposive sampling, respondent-driven sampling, and mixed purposive sampling. We review the relative advantages and drawbacks of the three methods in terms of access to the targeted population, methods of recruitment, size of the sample pool, randomness of the sample, generalizability of results, and researchers' control over the process.