A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a “pseudo–factorized” form which makes asymptotic analysis simpler. In this brief note, we use those contour integral formulas to find the asymptotics of the two-point correlations. As expected, the term arising from the “shift–invariance” makes a non-trivial asymptotic contribution.

We propose a new regression model based on the extension of the generalized Rayleigh distribution. This regression model can be used to model survival data where the hazard rate function is increasing, decreasing, bathtub or unimodal-shaped. We employ a frequentist estimation procedure for the parameters of the proposed model. The predictive performance of the new model is compared with a machine learning approach based on random survival forests, where we explore model validation and computational aspects. We carry out simulation studies for different parameter settings, sample sizes, and censoring percentages, considering the new regression model and the machine learning methodology. Finally, we showcase our methods using real data from a medical case study.

Extreme expectiles recently found their high performance in estimation of financial tail risk as expectile is a unique risk measure of both coherence and elicitability. In view of the conditional heteroscedasticity phenomenon in financial data, this paper is devoted to estimation of extreme conditional and unconditional expectiles in linear GARCH models with heavy-tailed error. Estimates are used to assess VaR and MES in extreme cases. Precisely, we employ a mature sieve approximation method to fit linear GARCH models to the data and obtain estimators of conditional variances and residuals. Extreme expectiles of these residuals are used as estimators of counterparts of the errors, and then combining the estimators of conditional variances, estimators are given for the extreme conditional and unconditional expectiles of the whole model. Moreover, based on these expectiles estimators, conditional marginal expected shortfall is also estimated. Asymptotic theory for estimators is derived. A simulation study shows merits of our methods. Finally, the methods are applied to two real data sets.

In this article, we report the development of adjustments to the profile likelihood function based on the proposals of Severini [Severini, T. A., 2000. Likelihood Methods in Statistics] and Cox and Reid [Cox, D.R., Reid, N. 1987. Parameter orthogonality and approximate conditional inference 49, 1-39] in the log Birnbaum-Saunders regression model under both type II censoring and noncensoring. We obtained the profile and modified profile maximum likelihood estimators, calculated the confidence intervals of the asymptotic type and bootstrap percentile and conducted tests based on profile and modified profile likelihood ratio statistics. Through Monte Carlo simulations, we numerically evaluated the behaviors of point estimators under different scenarios, as well as the performance of the likelihood ratio tests based on the profile and modified profile likelihoods, in terms of size and power. The results showed that both the tests and the estimators based on modified versions of the profile likelihood developed had superior performance in small samples in comparison with the estimators based on the unmodified version. Finally, an application to real data is presented.

With reference to a linear model with correlated errors, we obtain an updation formula for the best linear unbiased estimator (BLUE) of the regression coefficients under multiple case-deletion. The generality and clarity of this formula, compared to its existing counterparts, facilitate its use. Specifically, the established formula leads to an attractive property of the best linear unbiased predictor (BLUP) of a multivariate predictand in terms of the invariance of the aforementioned BLUE as well as the residual sum of squares when the BLUP is substituted for actual observations. This property is illustrated with a numerical example on order statistics from a location-scale model.

In social networks, there is a paradox that an individual’s friends tend to have more friends than the individual. The friendship paradox is a summary statistic of networks that measures the strength of the paradox. It has many applications in network data analysis. As far as we know, theoretical properties of the friendship paradox are not well studied. In this paper, we derive the asymptotic distribution of the friendship paradox in a random geometric graph. After centering and scaling, the friendship paradox converges in law to a series of independent standard normal random variables. It is interesting that the limiting distribution is not the standard normal distribution.