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Abstract: Abstract The present work deals with the parameter estimation problem for an nth-order mixed fractional Brownian motion (fBm) of the form \(X(t)=\theta \mathcal {P}(t)+\alpha W(t)+\sigma B_H^n(t)\) , where W(t) is a Wiener process and \(B_H^n(t)\) is the nth-order fBm ( \(n\ge 2\) ) with Hurst index \(H\in (n-1,n)\) . By using power-variations method we estimate \(\alpha\) , then we build maximum likelihood estimators of the parameters \(\theta\) and \(\sigma\) . Both weak and almost sure behaviour of the proposed estimators are established. PubDate: 2023-03-14
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Abstract: Abstract Establishing equivalence of two treatments has received a lot attention in the pharmaceutical industry. For assessing equivalence of two survival curves, an elegant test is proposed by Wellek (Biometrics 49:877–881, 1993) under the Cox proportional hazards (PH) model. An alternative test based on the proportional odds (PO) model was proposed by Martinez et al. (Stat Methods Med Res 26:75–87, 2017). Recently, Shen (J Biopharm Stat 31:79–90, 2021) proposed a test for equivalence based on a semiparametric log transformation model, which can be used if neither the PH nor the PO assumptions hold. In this article, under the class of Box–Cox transformation models (BCTM), we propose an equivalence test for the difference of two survival functions. Under the class of BCTM, we show that the hypothesis of equivalence of two survival functions can be formulated as a two-sided test which involves only the treatment effect parameter. Simulation results show that the proposed test has satisfactory size and adequate power for finite sample. PubDate: 2023-03-01
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Abstract: Abstract Statistical analyses of seasonal variation are important in the medical and social sciences because the results from such analyses can help elucidate the environment’s impact on human activity, behavior, and health. Generally, we are concerned with a data set of just 12 frequencies over a one-year period, and both the sample size and the variation’s amplitude are small, features that complicate the analysis; to assist in these situations, statisticians have created specialized tests for such data. One of those tests is an optimal-power likelihood-ratio test, whose application can fail because of computational complications. We are interested in the practical application of the said likelihood-ratio test, and so we present previously unknown information about the following: (1) When is the likelihood-ratio test likely to fail, and what are the chances for such failure to happen' (2) If the likelihood-ratio test does fail, what other test should the researcher use' Also, we provide new insights as to when and why the likelihood-ratio test would fail. Thus, in this study, we round out and complete important information about the performance of the optimal-power likelihood-ratio test for seasonality. Our results are useful to researchers who plan to do an analysis of seasonal variation. PubDate: 2023-03-01
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Abstract: Abstract The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that allows for confidence statements to be made regarding the order of a finite mixture model. We construct finite sample tests, via data splitting and data swapping, for use in the STP, and we prove that such tests are consistent against fixed alternatives. Simulation studies and real data examples are used to demonstrate the performance of the finite sample tests-based STP, yielding practical recommendations of their use as confidence estimators in combination with point estimates such as the Akaike information or Bayesian information criteria. In addition, we demonstrate that a modification of the STP yields a method that consistently selects the order of a finite mixture model, in the asymptotic sense. Our STP is not only applicable for order selection of finite mixture models, but is also useful for making confidence statements regarding any sequence of nested models. PubDate: 2023-03-01
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Abstract: Abstract In order to describe the finite-range integer-valued time series data with dependent structure and excess zeros, we introduce a new binomial AR(1) process with an alternative generalized binomial thinning operator. Some probabilistic and statistical properties of this model are derived. Model parameters are estimated by conditional least squares method and conditional maximum likelihood method. The consistency and asymptotic normality of these estimators are studied. In addition, a real data analysis shows a better performance of the proposed model than other existing models. PubDate: 2023-03-01
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Abstract: Abstract In this paper, we investigate a non-parametric approach to compare two groups in microarray data. This is done using a threshold penalized-distance likelihood function, which is made up of a penalty and a suitable threshold distance, and is applicable when sample size is small or when the data is not normally distributed. We also use this function to classify new data. This is based on objects that are identified as differences between the two groups, not for all objects. We also study a real data application to illustrate our methods. PubDate: 2023-03-01
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Abstract: Abstract Common methods for Bayesian prior elicitation call for expert belief in the form of numerical summaries. However, certain challenges remain with such strategies. Drawing on recent advances made in graphical inference, we propose an interactive method and tool for prior elicitation in which experts express their belief through a sequence of selections between pairs of graphics, reminiscent of the common procedure used during eye examinations. The graphics are based on synthetic datasets generated from underlying prior models with carefully chosen parameters, instead of the parameters themselves. At each step of the process, the expert is presented with two familiar graphics based on these datasets, billed as hypothetical future datasets, and makes a selection regarding their relative likelihood. Underneath, the parameters that are used to generate the datasets are generated in a way that mimics the Metropolis algorithm, with the experts’ responses forming transition probabilities. Using the general method, we develop procedures for data models used regularly in practice: Bernoulli, Poisson, and Normal, though it extends to additional univariate data models as well. A free, open-source Shiny application designed for these procedures is also available online, helping promote best practice recommendations in myriad ways. The method is supported by simulation. PubDate: 2023-03-01
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Abstract: Abstract In this paper, we propose a weighted extension of the family of multivariate Generalized Asymmetric Laplace (GAL) distributions. This extension is formed as a variance-mean mixture of the multivariate normal distribution and the weighted gamma distribution. By using the weighted gamma distribution as the mixing distribution, the resulting family of weighted GAL (WGAL) distributions gains an additional parameter to further regulate kurtosis and tail thickness; this is an advantage over the family of GAL distributions for modeling data sets. In particular, this new parameter provides great flexibility in adjusting the kurtosis and tail thickness for some members of the GAL distributions family, since these distributions are the widely used members of the GAL family without any shape parameter regulating kurtosis and tail thickness. After defining the multivariate WGAL distributions family and constructing the probability density function, we give some special cases of the new family and examine various properties of the new distributions, such as linear transformations, conditional distributions, and multivariate kurtosis measure. We study the maximum likelihood (ML) estimation to estimate the parameters and describe an algorithm based on the expectation maximization (EM) principle to obtain the ML estimates. We also provide simulation studies and real data examples to explore the modeling capacity of some distributions belonging to the newly proposed family of distributions. PubDate: 2023-03-01
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Abstract: Abstract Asymptotically linear negative quadrant dependent (ALNQD) sequence is more general than negatively associated (NA) sequence and \(\rho ^*\) -mixing sequence. Based on ALNQD errors, the CUSUM estimator of mean change-point is studied with common conditions. We obtain a limiting distribution of CUSUM estimator, which can be used to judge the existence of mean change-point. Meanwhile, some weak and strong convergence rates are established for the CUSUM estimator of change-point. In addition, a data-driven algorithm of multiple change-point detection is given, which performs better than Lasso algorithm. Last, multiple change-point detection simulations and real data analysis illustrate the accuracy of our results. PubDate: 2023-03-01
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Abstract: Abstract This paper proposes an efficient approach to deal with the issue of estimating multiple quantile regression (MQR) model. The relationship between the multiple quantiles and within-subject correlation is accommodated to improve efficiency in the presence of nonignorable dropouts. We adopt empirical likelihood (EL) to estimate the MQR coefficients. To handle the identifiability issue caused by nonignorable dropouts, a nonresponse instrument is used to estimate the parameters involved in a propensity model. In addition, bias-corrected and smoothed generalized estimating equations are built by applying kernel smoothing and inverse probability weighting approach. Furthermore, in order to measure the within-subject correlation structure, the idea of quadratic inference function is also taken into account. Theoretical results indicate that the proposed estimator has asymptotic normality and the confidence regions for MQR coefficients are also derived. Numerical simulations and an application to real data are also presented to investigate the performance of our proposed method. PubDate: 2023-03-01
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Abstract: Abstract Mixed membership community detection is a challenging problem. In this paper, to detect mixed memberships, we propose a new method Mixed-SLIM which is a spectral clustering method on the symmetrized Laplacian inverse matrix under the degree-corrected mixed membership model. We provide theoretical bounds for the estimation error on the proposed algorithm and its regularized version under mild conditions. Meanwhile, we provide some extensions of the proposed method to deal with large networks in practice. These Mixed-SLIM methods outperform state-of-art methods in simulations and substantial empirical datasets for both community detection and mixed membership community detection problems. PubDate: 2023-03-01
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Abstract: Abstract A new active zero set descent algorithm is proposed for least absolute deviation (LAD) problems with generalized LASSO penalty. Zero set contains the terms in the cost function that are zero-valued at the solution. Unlike state-of-art numerical approximation strategies such as interior point method, user-chosen threshold value is not required by the proposed algorithm to identify the zero set. Moreover, no nested iteration is needed. The algorithm updates the zero set and basis search directions recursively until optimality conditions are satisfied. It is also shown that the proposed algorithm converges in finitely many steps. Extensive simulation studies and real data analysis are conducted to confirm the time-efficiency of our algorithm. PubDate: 2023-03-01
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Abstract: Abstract We derive non-asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non-parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first) Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with Lipschitz and strongly convex costs. PubDate: 2023-02-24
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Abstract: Abstract In this paper, we propose a procedure to test the independence of bivariate censored data, which is generic and applicable to any censoring types in the literature. To test the hypothesis, we consider a rank-based statistic, Kendall’s tau statistic. The censored data defines a restricted permutation space of all possible ranks of the observations. We propose the statistic, the average of Kendall’s tau over the ranks in the restricted permutation space. To evaluate the statistic and its reference distribution, we develop a Markov chain Monte Carlo (MCMC) procedure to obtain uniform samples on the restricted permutation space and numerically approximate the null distribution of the averaged Kendall’s tau. We numerically compare the power of our procedure to existing state of the art procedures in the literature under various censoring types. We apply the procedure to three real data examples with different censoring types, and compare the results with those by existing methods. PubDate: 2023-02-24
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Abstract: Abstract Standard binary classifiers that maximize the overall accuracy fail in fraud detection where very few fraud cases are concealed within a large number of normal ones, as the best accuracy is often achieved by ignoring all fraud cases. In such a scenario, a natural alternative is what we refer to as a fraud-detection support vector machine, which never fails to detect fraud during training. In this article, we propose the L \(_1\) -penalized fraud-detection SVM that is capable of efficiently detecting fraud cases and selecting informative variables simultaneously. We establish the piecewise linearity of the L \(_1\) -penalized fraud detection SVM as a function of the regularization parameter and then develop an efficient algorithm for computing its entire regularization paths, greatly facilitating its tuning. The advantages of the L \(_1\) -penalized fraud detection SVM and its path algorithm for fraud detection are numerically demonstrated using both simulated and real data sets. PubDate: 2023-02-21
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Abstract: Abstract We propose a Bayesian pathway selection method that allows the selection of pathways (sets of genes) directly related to a continuous response variable under a non-parametric hierarchical model framework. The fact that sets of genes effectively explain more the response variable than individual genes was the driving force behind this research. We utilize the stochastic search variable selection and kernel machine method to select effective pathways after adjusting clinical covariates effects. The selection of pathways simultaneously works compared to other methods, where pathways are analyzed separately. We show that the proposed model can successfully detect effective pathways associated with outcomes through simulation studies and real data application. PubDate: 2023-01-24
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Abstract: Abstract We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets. PubDate: 2023-01-23
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Abstract: Abstract In this paper, we propose a Bayesian additive Cox model for analyzing current status data based on the expectation–maximization variable selection method. This model concurrently estimates unknown parameters and identifies risk factors, which efficiently improves model interpretability and predictive ability. To identify risk factors, we assign appropriate priors on the indicator variables which denote whether the risk factors are included. By assuming partially linear effects of the covariates, the proposed model offers flexibility to account for the relationship between risk factors and survival time. The baseline cumulative hazard function and nonlinear effects are approximated via penalized B-splines to reduce the dimension of parameters. An easy to implement expectation–maximization algorithm is developed using a two-stage data augmentation procedure involving latent Poisson variables. Finally, the performance of the proposed method is investigated by simulations and a real data analysis, which shows promising results of the proposed Bayesian variable selection method. PubDate: 2023-01-22
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Abstract: Abstract We study the nonparametric deconvolution problem of cumulative distribution function when measurement errors are heteroscedastic and have known distributions. Using a Fourier-type deconvolution method, we propose an estimator for the target function that depends only on a regularization parameter. Our estimator achieves minimax optimal convergence rates when the errors are all either ordinary smooth or supersmooth. A simulation study is also conducted to illustrate the effectiveness of the proposed estimator. PubDate: 2023-01-21
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Abstract: Abstract The independence of irrelevant alternatives (IIA) property states that the ratio of any two choice probabilities in a set of alternatives is independent of the presence or absence of other alternatives. In the modeling of multinomial data, the IIA is not feasible. In this situation, the multinomial probit (MNP) model is a type of discrete choice model that is commonly used. Due to the identifiability problem and the positive-definiteness constraint, modeling the covariance matrix in the MNP is difficult. All existing methods use unidentifiable parameters in the covariance matrix to solve the unidentifiability problem and improve the rate of convergence of a data augmentation algorithm. These methods also use the inverse Wishart distribution, which is frequently insufficient (Barnard et al. Stat Sin 10(4):1281–1311, 2000). We employed variance-correlation decomposition to decompose the identifiable covariance matrix into standard deviations and a correlation matrix instead of using the unidentifiable covariance matrix. Hypersphere decomposition was also used to decompose the correlation matrix. Thus, the estimated covariance matrix satisfied the positive definiteness constraint. The performance of our proposed model was illustrated using a detergent dataset from market research. PubDate: 2022-12-03
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