Replication with MTurk of the experimental design by Gangadharan,Grossman, Jones & Leister (2018): Charitable giving across donor types

Understanding the motivations behind charitable giving and the identification of donor types have aroused growing interest among researchers. The economic literature has highlighted the model of pure altruist and subsequently the more realistic model of impure altruist or warm-glow giver. The need to distinguish and empirically identify these types of donors has given rise to some economic experiments. This paper - using the platform by Amazon's Mechanical Turk with a large sample of participants (N = 1062) - shows the findings of a near replication of the experimental design by Gangadharan et al. (2018). Results are consistent with the original study and confirm the validity of the procedure and the ability to replicate a critical feature of the original design.     

Methods for high-dimensional multivariate and multi-group repeated measures data under non-normality

Asymptotic tests for multivariate repeated measures are derived under non-normality and unspecified dependence structure. Notwithstanding their broader scope of application, the methods are particularly useful when a random vector of large number of repeated measurements are collected from each subject but the number of subjects per treatment group is limited. In some experimental situations, replicating the experiment large number of times could be expensive or infeasible. Although taking large number of repeated measurements could be relatively cheaper, due to within subject dependence the number of parameters involved could get large pretty quickly. Under mild conditions on the persistence of the dependence, we have derived asymptotic multivariate tests for the three testing problems in repeated measures analysis. The simulation results provide evidence in favour of the accuracy of the approximations to the null distributions.     

Lifetime Uncertainty and Time Preference

Despite Fisher's (1930) psychological intuitions of and the formal treatment given by Yaari (1965, Review of Economic Studies 32, 137), the intertemporal model of choice is mainly a model with certain lifetime. The purpose of this paper is to reconsider this assumption, starting from a very simple two-period model of choice with lifetime uncertainty. We examine the comparative statics of the model at the first two orders and replace the concept of `pure time preference' by taking into account the subjective treatment of the probability of survival. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the use of priors in goodness‐of‐fit tests

Priors are introduced into goodness‐of‐fit tests, both for unknown parameters in the tested distribution and on the alternative density. Neyman–Pearson theory leads to the test with the highest expected power. To make the test practical, we seek priors that make it likely a priori that the power will be larger than the level of the test but not too close to one. As a result, priors are sample size dependent. We explore this procedure in particular for priors that are defined via a Gaussian process approximation for the logarithm of the alternative density. In the case of testing for the uniform distribution, we show that the optimal test is of the U‐statistic type and establish limiting distributions for the optimal test statistic, both under the null hypothesis and averaged over the alternative hypotheses. The optimal test statistic is shown to be of the Cramér–von Mises type for specific choices of the Gaussian process involved. The methodology when parameters in the tested distribution are unknown is discussed and illustrated in the case of testing for the von Mises distribution. The Canadian Journal of Statistics 47: 560–579; 2019 © 2019 Statistical Society of Canada     

Small sample equivalence tests for exponentiality

We consider small sample equivalence tests for exponentialy. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require much larger sample sizes, in comparison with classical “difference tests,” to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of small sample equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. We perform small sample simulation studies to assess the bias of our various tests and show that all of the Bayes posteriors we consider are integrable. Our simulation studies show that the saddlepoint-approximated UMPU method performs remarkably well for small sample sizes and is the only method that consistently exhibits an empirical significance level close to the nominal 5% level.     

Generalized sequential ranks and tests of randomness

Generalized sequential ranks are defined and are proved to be independent and uniformly distributed under the hypothesis of randomness. By comparison with a Spear-MAsr-type statistic it is shown that in certain cases the test based on the sum of all sequential ranks is an asymptotically optimum test for trend against logistic regression. The test is equivalent to tests proposed by Jonckheere and Terpstra and has a high efficiency when compared with the optimal parametric test for normal regression alternatives.     

Goodness-of-Fit Tests Based on Correcting Moments of Entropy Estimators

In this article, we consider the entropy estimator introduced by Alizadeh Noughabi and Arghami (2010) and derive the nonparametric distribution function corresponding to our estimator as a piece-wise uniform distribution. We use the results to introduce goodness-of-fit tests for the normal and the exponential distributions. The critical values and powers for some alternatives are obtained by simulation. The powers of the proposed tests under various alternatives are compared with the competitors.     

Partial central subspace and sliced average variance estimation

Sliced average variance estimation is one of many methods for estimating the central subspace. It was shown to be more comprehensive than sliced inverse regression in the sense that it consistently estimates the central subspace under mild conditions while slice inverse regression may estimate only a proper subset of the central subspace. In this paper we extend this method to regressions with qualitative predictors. We also provide tests of dimension and a marginal coordinate hypothesis test. We apply the method to a data set concerning lakes infested by Eurasian Watermilfoil, and compare this new method to the partial inverse regression estimator.     

Measuring Measurement Error in Economic Time Series

A spectral decomposition method is described for obtaining an upper bound on the amount of measurement error in a time series. The method is applied to generated data and to M1b, real GNP, and the CPI. The bounds provide insight into both the amount of measurement error in these series and the stochastic specification of the errors.     

Kendall's tau for serial dependence

The authors show how Kendall's tau can be adapted to test against serial dependence in a univariate time series context. They provide formulas for the mean and variance of circular and noncircular versions of this statistic, and they prove its asymptotic normality under the hypothesis of independence. They present also a Monte Carlo study comparing the power and size of a test based on Kendall's tau with the power and size of competing procedures based on alternative parametric and nonparametric measures of serial dependence. In particular, their simulations indicate that Kendall's tau outperforms Spearman's rho in detecting first‐order autoregressive dependence, despite the fact that these two statistics are asymptotically equivalent under the null hypothesis, as well as under local alternatives.