Statistical Papers最新文献

Reinforcement learning policy evaluation problems are often modeled as finite or discounted/averaged infinite-horizon Markov Decision Processes (MDPs). In this paper, we study undiscounted off-policy evaluation for absorbing MDPs. Given the dataset consisting of i.i.d episodes under a given truncation level, we propose an algorithm (referred to as MWLA in the text) to directly estimate the expected return via the importance ratio of the state-action occupancy measure. The Mean Square Error (MSE) bound of the MWLA method is provided and the dependence of statistical errors on the data size and the truncation level are analyzed. The performance of the algorithm is illustrated by means of computational experiments under an episodic taxi environment

In clinical trials studying paired parts of a subject with binary outcomes, it is expected to collect measurements bilaterally. However, there are cases where subjects contribute measurements for only one part. By utilizing combined data, it is possible to gain additional information compared to using bilateral or unilateral data alone. With the combined data, this article investigates homogeneity tests of risk differences with the presence of stratification effects and proposes interval estimations of a common risk difference if stratification does not introduce underlying dissimilarities. Under Dallal’s model (Biometrics 44:253–257, 1988), we propose three test statistics and evaluate their performances regarding type I error controls and powers. Confidence intervals of a common risk difference with satisfactory coverage probabilities and interval length are constructed. Our simulation results show that the score test is the most robust and the profile likelihood confidence interval outperforms other methods proposed. Data from a study of acute otitis media is used to illustrate our proposed procedures.

It has previously been pointed out that Student’s t test, which assumes that samples are drawn from populations with equal standard deviations, can have an inflated Type I error rate if this assumption is violated. Hence it has been recommended that Welch’s t test should be preferred. In the context of carrying out gene-wise weighted burden tests for detecting association of rare variants with psoriasis we observe that Welch’s test performs unsatisfactorily. We show that if the assumption of normality is violated and observations follow a Poisson distribution, then with unequal sample sizes Welch’s t test has an inflated Type I error rate, is systematically biased and is prone to produce extremely low p values. We argue that such data can arise in a variety of real world situations and believe that researchers should be aware of this issue. Student’s t test performs much better in this scenario but a likelihood ratio test based on logistic regression models performs better still and we suggest that this might generally be a preferable method to test for a difference in distributions between two samples.

This research has been conducted using the UK Biobank Resource.

Abstract

In this paper, we propose a new scale-invariant test for linear hypothesis of mean vectors with heteroscedasticity in high-dimensional settings. Most existing tests impose strong conditions on covariance matrices so that null distributions of their tests are asymptotically normal, which restricts the application of test procedures. However, our proposed test has different null distributions under mild conditions. Additionally, the well-known Welch-Satterthwaite chi-square approximation we adopted can automatically mimic the shapes of the null distributions of the test statistic. The performances of the test are illustrated by simulation and real data in finite samples which show that it has robustness and is more powerful than three competitors.

We propose a general and relatively simple method to construct goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function, and it leads to test criteria that are convenient regarding applications and consistent against arbitrary deviations from the model under test. We emphasize goodness-of-fit tests for spherical distributions due to their importance in applications and the relative scarcity of available methods.

The increasing computational power has led to an increasing interest in Fisher’s test in social science. As the Fisher and Neyman inference are based on different principles there is also an increasing interest in understanding the differential features of the two procedures. For example, Young (2018) found that the Fisher test has better size properties than the Neyman test in the situation with influential observations. Ding (2017), on the other hand, showed that the asymptotic variance of the mean-difference estimator (MDE) under Fisher inference is larger than that under Neyman inference, and that the asymptotic Fisher test is less powerful than the t-test even for the simplest case of homogeneous effect. Since MDE plays an important role for policy evaluation, these latter results are a concern for using Fisher’s test as argued in Young (2018). With the aim of providing an understanding of the usefulness of the exact Fisher test for inference to the sample and to the population, this paper clarifies the results in Ding (2017). Using a novel Monte Carlo simulation following the same data generating processes as in Ding (2017), we demonstrate that the Fisher test has no worse power properties than the t-test even with heterogeneous effects.

This article considers the problem of nonparametric estimation of the regression function (r) in a functional regression model (Y = r(X) +varepsilon ) with a scalar response Y, a functional explanatory variable X, and a second order stationary error process (varepsilon ). Under some specific criteria, we construct a local linear kernel estimator of (r) from functional random design with correlated errors. The exact rates of convergence of mean squared error of the constructed estimator are established for both short and long range dependent error processes. Simulation studies are conducted on the performance of the proposed simple local linear estimator. Examples of time series data are considered.

In this paper, strong consistency of tail value-at-risk (TVaR) estimator under widely orthant dependent (WOD) samples is established, and a numerical simulation is performed to verify the validity of the theoretical results. To reveal the essence of the result, theoretical discussion on complete and complete moment convergence corresponding to the Baum–Katz law, as well as the Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for maximal weighted sums and maximal product sums of widely orthant dependent (WOD) random variables are investigated. The results obtained in the context extend the corresponding ones for independent and some dependent random variables.

The growing popularity of data heterogeneity motivates people to identify homogeneous subgroups with identical parameters. Meanwhile, in many fields of recent data science for some applications, such as personalized education and personalized marketing, the massive data are usually recorded as categorical or ordinal variables, which highlights the importance of performing subgroup analysis on those ordinal outcomes. In this paper, we propose a cumulative link model with subject-specific intercepts to detect and identify homogeneous subgroups through concave pairwise fusion penalty for ordinal response, where heterogeneity arises from some unknown or unobserved latent factors. The concave fusion method can simultaneously determine the number of subgroups, identify the group membership, and estimate the regression coefficients. An alternating direction method of multipliers algorithm with concave penalties for the generalized linear regression model with logit link is developed and its convergence property is studied. We also establish the oracle property of the proposed penalized estimator under some mild conditions. Our simulation studies show that the proposed method could recover the heterogeneous subgroup structure effectively when the response of interest is ordinal. Further, the advantages of our method are illustrated by the analysis on a Mathematics Student Performance Data Set of two public schools from the Alentejo region of Portugal.

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen’s d. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central t distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges’ g. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set.