COMPARING TESTS OF AUTOREGRESSIVE VERSUS MOVING AVERAGE ERRORS IN REGRESSION MODELS USING BAHADUR’S ASYMPTOTIC RELATIVE EFFICIENCY

ABSTRACT

The purpose of this paper is to use Bahadur's asymptotic relative efficiency measure to compare the performance of various tests of autoregressive (AR) versus moving average (MA) error processes in regression models. Tests to be examined include non-nested procedures of the models against each other, and classical procedures based upon testing both the AR and MA error processes against the more general autoregressive-moving average model.     

Quantile estimation in the proportional hazards model of random censorship

The asymptotic theory is given for quantile estimation in the proportional hazards model of random censorship. In this model, the tail of the censoring distribution function is some power of the tail of the survival distribution function. The quantile estimator is based on the maximum likelihood estimator for the survival time distribution, due to Abdushukurov, Cheng and Lin.     

An exhaustive numerical assessment of alternative unconditional tests of a binary treatment effect

For testing the effectiveness of a treatment on a binary outcome, a bewildering range of methods have been proposed. How similar are all these tests? What are their theoretical strengths and weaknesses? Which are to be recommended and what is a coherent basis for deciding? In this paper, we take seven standard but imperfect tests and apply three different methods of adjustment to ensure size control: maximization (M), restricted maximization (B) and bootstrap/estimation (E). Across a wide conditions, we compute exact size and power of the 7 basic and 21 adjusted tests. We devise two new measures of size bias and intrinsic power, and employ novel graphical tools to summarise a huge set of results. Amongst the 7 basic tests, Liebermeister’s test best controls size but can still be conservative. Amongst the adjusted tests, E-tests clearly have the best power and results are very stable across different conditions.     

A consistent estimator for logistic mixed effect models

We propose a consistent and locally efficient method of estimating the model parameters of a logistic mixed effect model with random slopes. Our approach relaxes two typical assumptions: the random effects being normally distributed, and the covariates and random effects being independent of each other. Adhering to these assumptions is particularly difficult in health studies where, in many cases, we have limited resources to design experiments and gather data in long‐term studies, while new findings from other fields might emerge, suggesting the violation of such assumptions. So it is crucial to have an estimator that is robust to such violations; then we could make better use of current data harvested using various valuable resources. Our method generalizes the framework presented in Garcia & Ma (2016) which also deals with a logistic mixed effect model but only considers a random intercept. A simulation study reveals that our proposed estimator remains consistent even when the independence and normality assumptions are violated. This contrasts favourably with the traditional maximum likelihood estimator which is likely to be inconsistent when there is dependence between the covariates and random effects. Application of this work to a study of Huntington's disease reveals that disease diagnosis can be enhanced using assessments of cognitive performance. The Canadian Journal of Statistics 47: 140–156; 2019 © 2019 Statistical Society of Canada     

高等数学教学中形象思维方法应用的探索

高等数学是变量数学,针对变量数学理论性、抽象性强的特点,本文用形象思维方法解决几个实例,探索了形象思维方法解决问题的优越性;提高学生理解问题、分析问题的实际能力。     

The validity of the chi-squared test when expected frequencies are small:A list of recent research references

A bibliography is given containing about 60 recent (chiefly post-1968) items on the validity of the chi-squared test for categorical data when the expected frequencies are small.     

Distributions of lrt associated with two-parameter exponential distributions

In this paper, an exact distribution of the likelihood ratio criterion for testing the equality of p two-parameter exponential distributions is obtained for unequal sample sizes in a computational form. A useful asymptotic expansion of the distribution is also obtained up to the order of n^-4 with the second term of the order of n^-3 and so can be used to obtain accurate approximations to the critical values of the test statistic even for comparatively small values of n where n is the combined sample size. In fact the first term alone which is a single beta distribution provides a powerful approximation for moderately large values of n.     

Markov Chain Monte Carlo for Exact Inference for Diffusions

ABSTRACT. We develop exact Markov chain Monte Carlo methods for discretely sampled, directly and indirectly observed diffusions. The qualification ‘exact’ refers to the fact that the invariant and limiting distribution of the Markov chains is the posterior distribution of the parameters free of any discretization error. The class of processes to which our methods directly apply are those which can be simulated using the most general to date exact simulation algorithm. The article introduces various methods to boost the performance of the basic scheme, including reparametrizations and auxiliary Poisson sampling. We contrast both theoretically and empirically how this new approach compares to irreducible high frequency imputation, which is the state‐of‐the‐art alternative for the class of processes we consider, and we uncover intriguing connections. All methods discussed in the article are tested on typical examples.