Statistical Papers最新文献

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

Abstract

Change point detection is an important area of scientific research and has applications in a wide range of fields. In this paper, we propose a sequential change point detection (SCPD) procedure for mean-shift change point models. Unlike classical feature selection based approaches, the SCPD method detects change points in the order of the conditional change sizes and makes full use of the identified change points information. The extended Bayesian information criterion (EBIC) is employed as the stopping rule in the SCPD procedure. We investigate the theoretical property of the procedure and compare its performance with other methods existing in the literature. It is established that the SCPD procedure has the property of detection consistency. Simulation studies and real data analyses demonstrate that the SCPD procedure has the edge over the other methods in terms of detection accuracy and robustness.

This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression.

In this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

The bootstrap method relies on resampling from the empirical distribution to provide inferences about the population with a distribution F. The empirical distribution serves as an approximation to the population. It is possible, however, to resample from another approximating distribution of F to conduct simulation-based inferences. In this paper, we utilize representative points to form an alternative approximating distribution of F for resampling. The representative points in terms of minimum mean squared error from F have been widely applied to numerical integration, simulation, and the problems of grouping, quantization, and classification. The method of resampling via representative points can be used to estimate the sampling distribution of a statistic of interest. A basic theory for the proposed method is established. We prove the convergence of higher-order moments of the new approximating distribution of F, and establish the consistency of sampling distribution approximation in the cases of the sample mean and sample variance under the Kolmogorov metric and Mallows–Wasserstein metric. Based on some numerical studies, it has been shown that the proposed resampling method improves the nonparametric bootstrap in terms of confidence intervals for mean and variance.

Abstract

Cattel’s (Multivar Behav Res 1:245–276, 1966) heuristic determines the number of factors as the elbow point between ‘steep’ and ‘not steep’ in the scree plot. In contrast, an elbow is by definition absent in points on a hyberbole with corresponding equisized surfaces. We formalize this heuristic and propose a criterion to determine the number of factors by comparing surfaces under the scree plot. Monte Carlo simulations shows that the finite-sample properties of our proposed criterion outperform benchmarks in the dynamic factor model literature.

In this paper, we focus on overlapping community detection and propose an efficient semi-orthogonal nonnegative matrix tri-factorization (semi-ONMTF) algorithm. This method factorizes a matrix X into an orthogonal matrix U, a nonnegative matrix B, and a transposed matrix (U^mathrm {scriptscriptstyle T} ). We use the Cayley Transformation to maintain strict orthogonality of U that each iteration stays on the Stiefel Manifold. This algorithm is computationally efficient because the solutions of U and B are simplified into a matrix-wise update algorithm. Applying this method, we detect overlapping communities by the belonging coefficient vector and analyse associations between communities by the unweighted network of communities. We conduct simulations and applications to show that the proposed method has wide applicability. In a real data example, we apply the semi-ONMTF to a stock data set and construct a directed association network of companies. Based on the modularity for directed and overlapping communities, we obtain five overlapping communities, 17 overlapping nodes, and five outlier nodes in the network. We also discuss the associations between communities, providing insights into the overlapping community detection on the stock market network.

Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which are frequently burdened with multiple imperfections. Often the underlying imprecision or vagueness can be suitably described in terms of fuzzy numbers which enable also the capture of subjectivity. On the other hand, due to the random nature of the experimental data, the tools for their description must take into account their statistical nature. In this way, we come to random fuzzy numbers that model fuzzy data and are also solidly formalized within the probabilistic setting. In this contribution, we introduce the so-called LR random fuzzy numbers that can be used in various Monte-Carlo simulations on fuzzy data. The proposed method of generating fuzzy numbers with membership functions given by probability densities is both simple and rich, well-grounded mathematically, and has a high application potential.