Statistical Papers最新文献

Negative binomial related distributions have been widely used in practice. The calculation of the corresponding Fisher information matrices involves the expectation of trigamma function values which can only be calculated numerically and approximately. In this paper, we propose a trigamma-free approach to approximate the expectations involving the trigamma function, along with theoretical upper bounds for approximation errors. We show by numerical studies that our approach is highly efficient and much more accurate than previous methods. We also apply our approach to compute the Fisher information matrices of zero-inflated negative binomial (ZINB) and beta negative binomial (ZIBNB) probabilistic models, as well as ZIBNB regression models.

In this work, we develop two stable estimators for solving linear functional regression problems. It is well known that such a problem is an ill-posed stochastic inverse problem. Hence, a special interest has to be devoted to the stability issue in the design of an estimator for solving such a problem. Our proposed estimators are based on combining a stable least-squares technique and a random projection of the slope function (beta _0(cdot )in L^2(J),) where J is a compact interval. Moreover, these estimators have the advantage of having a fairly good convergence rate with reasonable computational load, since the involved random projections are generally performed over a fairly small dimensional subspace of (L^2(J).) More precisely, the first estimator is given as a least-squares solution of a regularized minimization problem over a finite dimensional subspace of (L^2(J).) In particular, we give an upper bound for the empirical risk error as well as the convergence rate of this estimator. The second proposed stable LFR estimator is based on combining the least-squares technique with a dyadic decomposition of the i.i.d. samples of the stochastic process, associated with the LFR model. In particular, we provide an (L^2)-risk error of this second LFR estimator. Finally, we provide some numerical simulations on synthetic as well as on real data that illustrate the results of this work. These results indicate that our proposed estimators are competitive with some existing and popular LFR estimators.

Traditionally, common testing problems are formalized in terms of a precise null hypothesis representing an idealized situation such as absence of a certain “treatment effect”. However, in most applications the real purpose of the analysis is to assess evidence in favor of a practically relevant effect, rather than simply determining its presence/absence. This discrepancy leads to erroneous inferential conclusions, especially in case of moderate or large sample size. In particular, statistical significance, as commonly evaluated on the basis of a precise hypothesis low p value, bears little or no information on practical significance. This paper presents an innovative approach to the problem of testing the practical relevance of effects. This relies upon the proposal of a general method for modifying standard tests by making them suitable to deal with appropriate interval null hypotheses containing all practically irrelevant effect sizes. In addition, when it is difficult to specify exactly which effect sizes are irrelevant we provide the researcher with a benchmark value. Acceptance/rejection can be established purely by deciding on the (ir)relevance of this value. We illustrate our proposal in the context of many important testing setups, and we apply the proposed methods to two case studies in clinical medicine. First, we consider data on the evaluation of systolic blood pressure in a sample of adult participants at risk for nutritional deficit. Second, we focus on a study of the effects of remdesivir on patients hospitalized with COVID-19.

Functional time series model has been the subject of the most research in recent years, and since functional data is infinite dimensional, dimension reduction is essential for functional time series. However, the majority of the existing dimension reduction methods such as the functional principal component and fixed basis expansion are unsupervised and typically result in information loss. Then, the functional time series model has an urgent need for a supervised dimension reduction method. The functional sufficient dimension reduction method is a supervised technique that adequately exploits the regression structure information, resulting in minimal information loss. Functional sliced inverse regression (FSIR) is the most popular functional sufficient dimension reduction method, but it cannot be applied directly to functional time series model. In this paper, we examine a functional time series model in which the response is a scalar time series and the explanatory variable is functional time series. We propose a novel supervised dimension reduction technique for the regression model by combining the FSIR and blind source separation methods. Furthermore, we propose innovative strategies for selecting the dimensionality of dimension reduction space and the lags of the functional time series. Numerical studies, including simulation studies and a real data analysis are show the effectiveness of the proposed methods.

In this paper, we advance the application of empirical likelihood (EL) for missing response problems. Inspired by remedies for the shortcomings of EL for parameter hypothesis testing, we modify the EL approach used for statistical inference on the mean response when the response is subject to missing behavior. We propose consistent mean estimators, and associated confidence intervals. We extend the approach to estimate the average treatment effect in causal inference settings. We detail the analogous estimators for average treatment effect, prove their consistency, and example their use in estimating the average effect of smoking on renal function of the patients with atherosclerotic renal-artery stenosis and elevated blood pressure, chronic kidney disease, or both. Our proposed estimators outperform the historical mean estimators under missing responses and causal inference settings in terms of simulated relative RMSE and coverage probability on average.

This paper explores a methodology for dimension reduction in regression models for a treatment outcome, specifically to capture covariates’ moderating impact on the treatment-outcome association. The motivation behind this stems from the field of precision medicine, where a comprehensive understanding of the interactions between a treatment variable and pretreatment covariates is essential for developing individualized treatment regimes (ITRs). We provide a review of sufficient dimension reduction methods suitable for capturing treatment-covariate interactions and establish connections with linear model-based approaches for the proposed model. Within the framework of single-index regression models, we introduce a sparse estimation method for a dimension reduction vector to tackle the challenges posed by high-dimensional covariate data. Our methods offer insights into dimension reduction techniques specifically for interaction analysis, by providing a semiparametric framework for approximating the minimally sufficient subspace for interactions.

Estimating the mean of a population is a recurrent topic in statistics because of its multiple applications. If previous data is available, or the distribution of the deviation between the measurements and the mean is known, it is possible to perform such estimation by using L-statistics, whose optimal linear coefficients, typically referred to as weights, are derived from a minimization of the mean squared error. However, such optimal weights can only manage sample sizes equal to the one used to derive them, while in real-world scenarios this size might slightly change. Therefore, this paper proposes a method to overcome such a limitation and derive approximations of flexible-dimensional optimal weights. To do so, a parametric family of functions based on extreme value reductions and amplifications is proposed to be adjusted to the cumulative optimal weights of a given sample from a symmetric distribution. Then, the application of Yager’s method to derive weights for ordered weighted average (OWA) operators allows computing the approximate optimal weights for sample sizes close to the original one. This method is justified from the theoretical point of view by proving a convergence result regarding the cumulative weights obtained for different sample sizes. Finally, the practical performance of the theoretical results is shown for several classical symmetric distributions.

Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). But there are few works focusing on matrix-form data with measurement error (ME), since tensor in conjunction with ME is relatively complex in structure. In this paper we introduce a mvGLM to primarily explore the influence of ME in the model with matrix-form data. We calculate the asymptotic bias based on error-prone mvGLM, and then develop bias-correction methods to tackle the affect of ME. Statistical properties for all methods are established, and the practical performance of all methods is further evaluated in analysis on synthetic and real data sets.

The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show strong consistency of different quantile estimators and we study the Bahadur representation for each of the quantile estimators, when the sample is taken from NA, (varphi ), (rho ^*), (rho )-mixing population.

Memory-type control charts are widely used for monitoring small to moderate shifts in the process parameter(s). In the present article, we present an exponentiated exponentially weighted moving average (Exp-EWMA) control chart that weights the past observations of a process using an exponentiated function. We evaluated the run-length characteristics of the Exp-EWMA chart via Monte Carlo simulations. A comparison study versus the CUSUM, EWMA and extended EWMA (EEWMA) charts under similar in-control (IC) run-length properties demonstrates that the Exp-EWMA chart is more effective for detecting small and, under certain circumstances, moderate shifts for both the zero-state and steady-state cases. Moreover, the Exp-EWMA chart has better zero-state out-of-control (OOC) performance than an EWMA chart with smoothing parameter equal to the limit to the infinity of the exponentiated function, while the two charts perform similarly for the steady-state case. Finally, it is shown that the Exp-EWMA chart is more IC robust than its competitors under several non-normal distributions. Two examples are provided to explain the implementation of the proposed chart