A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects

In this paper, we present a test of independence between the response variable, which can be discrete or continuous, and a continuous covariate after adjusting for heteroscedastic treatment effects. The method involves first augmenting each pair of the data for all treatments with a fixed number of nearest neighbours as pseudo‐replicates. Then a test statistic is constructed by taking the difference of two quadratic forms. The statistic is equivalent to the average lagged correlations between the response and nearest neighbour local estimates of the conditional mean of response given the covariate for each treatment group. This approach effectively eliminates the need to estimate the nonlinear regression function. The asymptotic distribution of the proposed test statistic is obtained under the null and local alternatives. Although using a fixed number of nearest neighbours pose significant difficulty in the inference compared to that allowing the number of nearest neighbours to go to infinity, the parametric standardizing rate for our test statistics is obtained. Numerical studies show that the new test procedure has robust power to detect nonlinear dependency in the presence of outliers that might result from highly skewed distributions. The Canadian Journal of Statistics 38: 408–433; 2010 © 2010 Statistical Society of Canada     

Profile—Educational Attainments of ASA Members, 1964

The lognormal distribution is useful for approximating the distributions of such input variables as costs, sales, market share, etc. required in Monte Carlo simulations of business decisions. An easy way to represent such distributions is by the tenth and ninetieth percentiles and the mode. Such representation, however, does not permit direct calculation of the usual characterizing parameters (θ, γ, and δ). An empirically-determined rational function is given by which the median can be approximated from the mode, which then permits direct calculation of θ, γ, and δ.     

ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX

Sample covariance matrices play a central role in numerous popular statistical methodologies, for example principal components analysis, Kalman filtering and independent component analysis. However, modern random matrix theory indicates that, when the dimension of a random vector is not negligible with respect to the sample size, the sample covariance matrix demonstrates significant deviations from the underlying population covariance matrix. There is an urgent need to develop new estimation tools in such cases with high‐dimensional data to recover the characteristics of the population covariance matrix from the observed sample covariance matrix. We propose a novel solution to this problem based on the method of moments. When the parametric dimension of the population spectrum is finite and known, we prove that the proposed estimator is strongly consistent and asymptotically Gaussian. Otherwise, we combine the first estimation method with a cross‐validation procedure to select the unknown model dimension. Simulation experiments demonstrate the consistency of the proposed procedure. We also indicate possible extensions of the proposed estimator to the case where the population spectrum has a density.     

Validating a Korean Version of the Drug Abuse Screening Test-10 (DAST-10)

ABSTRACT

There are no screening instruments for adults in the Korean language that are specific to drugs other than alcohol and tobacco. The purpose of this study is to validate the Korean version of the Drug Abuse Screening Test-10 (DAST-10). The Korean version of the DAST-10 was validated with 1,000 adults including general adults and at-risk adults. The results indicated that the Korean version of the DAST-10 was unidimensional similar to its English-language counterpart and showed satisfactory internal consistency reliability and convergent validity. The results also showed that the Korean version demonstrated optimal performance at a cutoff score of 2, which is the same as that of its English-language counterpart. It is expected that as the development of Korean-language instruments measuring alcohol problems contributes to the expansion of related research, the development of the Korean version of the DAST-10 will facilitate research on various topics related to substance abuse in Korea. Validation with Korean adults identified as substance abusers is needed to improve the ability of the Korean version to correctly identify substance-abusing adults.     

Modeling U.S. monetary policy during the global financial crisis and lessons for Covid-19

The paper formulates the modeling of unconventional monetary policy and critically evaluates its effectiveness to address the Global Financial Crisis. We begin with certain principles guiding general scientific modeling and focus on Milton Friedman's 1968 Presidential Address that delineates the strengths and limitations of monetary policy to pursue certain goals. The modeling of monetary policy with its novelty of quantitative easing to target unusually high unemployment is evaluated by a Markov switching econometric model using monthly data for the period 2002–2015. We conclude by relating the lessons learned from unconventional monetary policy during the Global Financial Crisis to the recent bold initiatives of the Fed to mitigate the economic and financial impact of the Covid-19 pandemic on U.S. households and businesses.     

A new approach for joint modelling of longitudinal measurements and survival times with a cure fraction

The joint analysis of longitudinal measurements and survival data is useful in clinical trials and other medical studies. In this paper, we consider a joint model which assumes a linear mixed $tt$ model for longitudinal measurements and a promotion time cure model for survival data and links these two models through a latent variable. A semiparametric inference procedure with an EM algorithm implementation is developed for the parameters in the joint model. The proposed procedure is evaluated in a simulation study and applied to analyze the quality of life and time to recurrence data from a clinical trial on women with early breast cancer. The Canadian Journal of Statistics 40: 207–224; 2012 © 2012 Statistical Society of Canada     

Nonparametric hierarchical Bayes analysis of binomial data via Bernstein polynomial priors

For binomial data analysis, many methods based on empirical Bayes interpretations have been developed, in which a variance‐stabilizing transformation and a normality assumption are usually required. To achieve the greatest model flexibility, we conduct nonparametric Bayesian inference for binomial data and employ a special nonparametric Bayesian prior—the Bernstein–Dirichlet process (BDP)—in the hierarchical Bayes model for the data. The BDP is a special Dirichlet process (DP) mixture based on beta distributions, and the posterior distribution resulting from it has a smooth density defined on [0, 1]. We examine two Markov chain Monte Carlo procedures for simulating from the resulting posterior distribution, and compare their convergence rates and computational efficiency. In contrast to existing results for posterior consistency based on direct observations, the posterior consistency of the BDP, given indirect binomial data, is established. We study shrinkage effects and the robustness of the BDP‐based posterior estimators in comparison with several other empirical and hierarchical Bayes estimators, and we illustrate through examples that the BDP‐based nonparametric Bayesian estimate is more robust to the sample variation and tends to have a smaller estimation error than those based on the DP prior. In certain settings, the new estimator can also beat Stein's estimator, Efron and Morris's limited‐translation estimator, and many other existing empirical Bayes estimators. The Canadian Journal of Statistics 40: 328–344; 2012 © 2012 Statistical Society of Canada     

Information borrowing methods for covariate‐adjusted ROC curve

In medical diagnostic testing problems, the covariate adjusted receiver operating characteristic (ROC) curves have been discussed recently for achieving the best separation between disease and control. Due to various restrictions such as cost, the availability of patients, and ethical issues quite frequently only limited information is available. As a result, we are unlikely to have a large enough overall sample size to support reliable direct estimations of ROCs for all the underlying covariates of interest. For example, some genetic factors are less commonly observable compared with others. To get an accurate covariate adjusted ROC estimation, novel statistical methods are needed to effectively utilize the limited information. Therefore, it is desirable to use indirect estimates that borrow strength by employing values of the variables of interest from neighbouring covariates. In this paper we discuss two semiparametric exponential tilting models, where the density functions from different covariate levels share a common baseline density, and the parameters in the exponential tilting component reflect the difference among the covariates. With the proposed models, the estimated covariate adjusted ROC is much smoother and more efficient than the nonparametric counterpart without borrowing information from neighbouring covariates. A simulation study and a real data application are reported. The Canadian Journal of Statistics 40: 569–587; 2012 © 2012 Statistical Society of Canada     

Competitive conditions in the Central and Eastern European banking systems

The aim of this study is to conduct an empirical analysis of the competitive conditions in the banking systems of Central and Eastern European countries. The well-known model of Panzar and Rosse [1] is implemented on bank-level data over the period 1999–2006. The estimates based on the separate country panels suggest a wide variation in the competitive conditions of the banking systems examined, with some being characterized as (monopolistically) competitive and other as non-competitive. Finally, the results from the full sample indicate that bank revenue is substantially influenced by structural and macroeconomic conditions.