Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

Pearson's system is a rich class of models that includes many classical univariate distributions. It comprises all continuous densities whose logarithmic derivative can be expressed as a ratio of quadratic polynomials governed by a vector $��\beta �$ of coefficients. The estimation of a Pearson density is challenging, as small variations in $��\beta �$ can induce wild changes in the shape of the corresponding density $��{�f�}_{�\beta �}�$. The authors show how to estimate $��\beta �$ and $��{�f�}_{�\beta �}�$ effectively through a penalized likelihood procedure involving differential regularization. The approach combines a penalized regression method and a profiled estimation technique. Simulations and an illustration with S&P 500 data suggest that the proposed method can improve market risk assessment substantially through value-at-risk and expected shortfall estimates that outperform those currently used by financial institutions and regulators.

Nancy Reid was born in September 1952 in Niagara Falls, Canada. She graduated from the University of Waterloo with a Bachelor in Mathematics and a Major in Statistics in 1974. She studied statistics at the University of British Columbia (UBC) where she obtained a Master's in Applied Mathematics in 1976, and at Stanford University where she graduated with a PhD in Statistics in 1979. After spending one year at Imperial College London visiting Sir David Cox, she joined UBC as an Assistant Professor in the Department of Mathematics, and in 1986 she moved to the University of Toronto as a faculty member in the Department of Statistics (now Statistical Sciences) where she has been ever since including serving as Chair between 1997 and 2002. At the time of writing, Nancy has authored over 100 papers and 5 books, including seminal developments in conditional inference, higher-order asymptotics, composite likelihood, and Bayesian inference. Her outstanding contributions to statistics have been recognized nationally and internationally with many awards, including the President's Award of the Committee of Presidents of Statistical Societies (COPSS), the Gold Medal awarded by the Statistical Society of Canada (SSC), and being elected Foreign Associate of the National Academy of Sciences. In 2017, the International Statistical Review published Nancy's conversation with Ana Maria Staicu [Staicu, A. M. (2017). Interview with Nancy Reid. International Statistical Review, 85(3), 381-403.], which had a biographical emphasis. Since then, Nancy has continued to support the discipline of statistics in important ways, such as by serving as Director of the Canadian Statistical Sciences Institute (CANSSI) (2015–2019) and Co-chair of the Institute of Mathematical Statistics' Committee on Ethics (2018–2020). Her research activity continues to be celebrated with important awards such as Fellowship of the Royal Society of London (2018), the inaugural Hollander Distinguished Lectureship at Florida State University (2020), the Distinguished Achievement Award (and Lectureship) from COPSS (2022), and the Guy Medal in Gold from the Royal Statistical Society (2022). In May 2022, the Department of Statistical Sciences at the University of Toronto, in collaboration with CANSSI and the SSC, organized a one-day conference, “Statistics at Its Best”, in honour of Nancy's 70th birthday. This conversation took place in Toronto around the time of the event. Its focus is on Nancy's views on building a career in statistics, and the challenges and opportunities statisticians encounter within the rapidly evolving data science ecosystem.

To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling approach under measurement constraints was developed to meet this challenge. This method uses the inverses of optimal sampling probabilities to reweight the objective function, which assigns smaller weights to the more important data points. Thus, the estimation efficiency of the resulting estimator can be improved. In this paper, we propose an unweighted estimating procedure based on optimal subsamples to obtain a more efficient estimator. We obtain the unconditional asymptotic distribution of the estimator via martingale techniques without conditioning on the pilot estimate, which has been less investigated in the existing subsampling literature. Both asymptotic results and numerical results show that the unweighted estimator is more efficient in parameter estimation.

In a one-component partial least squares fit of a linear regression model, we find the asymptotic normal distribution, as the sample size and number of predictors approach infinity, of a user-selected univariate linear combination of the coefficient estimator and give corresponding asymptotic confidence and prediction intervals. Simulation studies and an analysis of a dopamine dataset are used to support our theoretical asymptotic results and their practical application.

Representations of measures of concordance in terms of Pearson's correlation coefficient are studied. All transforms of random variables are characterized such that the correlation coefficient of the transformed random variables is a measure of concordance. Gini's gamma then is generalized and it is shown that the resulting generalized Gini's gamma can be represented as a mixture of measures of concordance that are Pearson's correlation coefficients of transformed random variables. As an application of this correlation mixture representation of generalized Gini's gamma, lower and upper bounds of the compatible set of generalized Gini's gamma, i.e., the collection of all square matrices of pairwise generalized Gini's gammas, are derived.

In dominated parametric statistical models, confidence sequences provide conservatively valid frequentist inference directly from a likelihood ratio. They ensure a specific mode of replicability when inference is performed on accumulating data: inferential conclusions that are compatible with a guaranteed probability when the sample is enlarged, in the form of overlapping confidence regions. Here we consider both Robbins' mixture confidence sequences and running maximum likelihood confidence sequences recently considered by Wasserman, Ramdas, and Balakrishnan. We compare through simulation the replicability properties of the two kinds of confidence sequences, evaluating, along a prospected enlargement of the sample, the frequency of incompatible estimation intervals and the frequency of failure of simultaneous coverage of the true parameter value. Moreover, we propose a shortcut to extend the application of mixture confidence sequences to pseudo-likelihoods, in particular to composite likelihood. The main assumption required is that normal asymptotic theory offers a good approximation to the density of the maximizer of the pseudo-likelihood. When inference is about a scalar parameter of interest, the computation of the proposed sequence of confidence intervals is straightforward. The method is illustrated by an example with replicability properties evaluated through simulation.

Two-sample hypothesis testing, as a fundamental problem in statistical inference, seeks to detect the difference between two probability measures and has numerous real-world applications. Current test procedures for multivariate two-sample problems typically rely on angles and lengths in a Euclidean space, or lengths in a unit hypersphere after representing data with the spherical model. This article introduces a hyperbolic divergence based on hyperbolic lengths in hyperbolic geometry, as well as a subsequent nonparametric approach to testing the multivariate two-sample problem. We investigate the properties of our test procedure and discover that our hyperbolic divergence statistic is strongly consistent and consistent against all other alternatives; we also demonstrate that its limit distribution is an infinite mixture of $�{�\chi �}^{�2�}$ distributions under the null hypothesis and a normal distribution under the alternative hypothesis. To calculate the $��P�$-value, we employ the permutation method. Furthermore, in numerical studies, we compare our method with several nonparametric procedures under various distributional assumptions and alternatives. We discover that our test procedure has some advantages when the distributions' complex correlation structures differ. Finally, we examine one real data set to show how our method can be used to test two-sample heterogeneity.

We develop two joint tests for the parametric drift and volatility functions of a diffusion model based on empirical processes. One key feature of our joint tests is that they account for different convergence rates of parameter estimators. The tests are of classical Kolmogorov–Smirnov and Cramér–von Mises types, and are asymptotically distribution free. The proposed tests have nontrivial power against a class of local alternatives with different convergence rates for the drift and volatility terms. Monte Carlo simulations show that the tests perform quite well in finite samples and outperform the nonparametric test of Hong and Li. The new tests are applied to EUR/USD exchange rate data and generate some interesting empirical findings that are consistent with our theoretical results and simulation studies.

Quantile regression for right- or left-censored outcomes has attracted attention due to its ability to accommodate heterogeneity in regression analysis of survival times. Rank-based inferential methods have desirable properties for quantile regression analysis, but censored data poses challenges to the general concept of ranking. In this article, we propose a notion of censored quantile regression rank scores, which enables us to construct rank-based tests for quantile regression coefficients at a single quantile or over a quantile region. A model-based bootstrap algorithm is proposed to implement the tests. We also illustrate the advantage of focusing on a quantile region instead of a single quantile level when testing the effect of certain covariates in a quantile regression framework.