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Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2021年第4期63卷 579-605页

作者： Liu, Pengyi Tian, Guo-Liang Yuen, Kam Chuen Zhang, Chi Tang, Man-Lai Yunnan Univ Finance & Econ Dept Stat Kunming 650221 Yunnan Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen 518055 Guangdong Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Pokfulam Rd Hong Kong Peoples R China Shenzhen Univ Coll Econ Shenzhen 518055 Guangdong Peoples R China Brunel Univ London Coll Engn Design & Phys Sci Dept Math Kingston Lane Uxbridge UB8 3PH Middx England

Outcomes in the form of rates, fractions, proportions and percentages often appear in various fields. Existing beta and simplex distributions are frequently unable to exhibit satisfactory performances in fitting such continuous data. This paper aims to develop the normalised inverse Gaussian (N-IG) distribution proposed by Lijoi, Mena & Prunster (2005, Journal of the American Statistical Association, 100, 1278-1291) as a new tool for analysing continuous proportional data in (0,1) and renames the N-IG as proportional inverse Gaussian (PIG) distribution. Our main contributions include: (i) To overcome the difficulty of an integral in the PIG density function, we propose a novel minorisation-maximisation (mm) algorithm via the continuous version of Jensen's inequality to calculate the maximum likelihood estimates of the parameters in the PIG distribution;(ii) We also develop an mm algorithm aided by the gradient descent algorithm for the PIG regression model, which allows us to explore the relationship between a set of covariates with the mean parameter;(iii) Both the comparative studies and the real data analyses show that the PIG distribution is better when comparing with the beta and simplex distributions in terms of the AIC, the Cramer-von Mises and the Kolmogorov-Smirnov tests. In addition, bootstrap confidence intervals and testing hypothesis on the symmetry of the PIG density are also presented. Simulation studies are conducted and the hospital stay data of Barcelona in 1988 and 1990 are analysed to illustrate the proposed methods.

关键词： AIC continuous proportional data mm algorithm proportional inverse Gaussian distribution simplex distribution

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Fast QLB algorithm and hypothesis tests in logistic model for ophthalmologic bilateral correlated data

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JOURNAL OF BIOPHARMACEUTICAL STATISTICS 2021年第1期31卷 91-107页

作者： Lin, Yi-Qi Zhang, Yu-Shun Tian, Guo-Liang Ma, Chang-Xing Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen 518055 Guangdong Peoples R China SUNY Buffalo Dept Biostat Buffalo NY USA

In ophthalmologic or otolaryngologic studies, bilateral correlated data often arise when observations involving paired organs (e.g., eyes, ears) are measured from each subject. Based on Donner's model , in this paper, we focus on investigating the relationship between the disease probability and covariates (such as ages, weights, gender, and so on) via the logistic regression for the analysis of bilateral correlated data. We first propose a newminorization-maximization(mm) algorithm and a fastquadratic lower bound(QLB) algorithm to calculate the maximum likelihood estimates of the vector of regression coefficients, and then develop three large-sample tests (i.e., the likelihood ratio test, Wald test, and score test) to test if covariates have a significant impact on the disease probability. Simulation studies are conducted to evaluate the performance of the proposed fast QLB algorithm and three testing methods. A real ophthalmologic data set in Iran is used to illustrate the proposed methods.

关键词： Assembly and decomposition technique bilateral correlated data fast QLB algorithm logistic regression model mm algorithm ophthalmologic study

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Squared normal model and its generalization for the analysis of skewed positive data

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COmmUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年

作者： Liu, Xuanyu Zhang, Chi Yuen, Kam Chuen Tian, Guo-Liang Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Peoples R China Shenzhen Univ Coll Econ Shenzhen Guangdong Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen Peoples R China

To model skewed positive data with high kurtosis, this paper proposes, a new squared normal (SQN) distribution, which is constructed by squaring the normal random variable with non-zero mean and non-unit variance. The SQN distribution can be regarded as an extension of the chi-squared distribution, which cannot be applied to directly modeling real-life data. Some distributional properties, parameter estimation methods and hypothesis testings are investigated for the SQN distribution itself and the corresponding regression model. Furthermore, a generalization to a squared skew-normal (SSN) distribution is proposed by incorporating an additional skew parameter, improving the flexibility of the model. Finally, simulation experiments are conducted and a real data set is analyzed to demonstrate the proposed methodologies.

关键词： mm algorithm newton-raphson algorithm skewed positive data squared normal distribution squared skew-normal distribution

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Demand estimation from sales transaction data: practical extensions

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JOURNAL OF REVENUE AND PRICING MANAGEMENT 2021年第3期20卷 276-300页

作者： Remenyi, Norbert Luo, Xiaodong Sabre 3150 Sabre Dr Southlake TX 76092 USA Shenzhen Res Inst Big Data Shenzhen Guangdong Peoples R China

In this paper, we discuss practical limitations of the standard choice-based demand models used in the literature to estimate demand from sales transaction data. We present modifications and extensions of the models and discuss data preprocessing and solution techniques which are useful for practitioners dealing with sales transaction data. Among these, we present an algorithm to split sales transaction data observed under partial availability, we extend a popular Expectation Maximization (EM) algorithm for non-homogeneous product sets, and we develop two iterative optimization algorithms which can handle much of the extensions discussed in the paper.

关键词： Demand estimation Demand untruncation Multinomial logit model EM algorithm mm algorithm Frank-Wolfe method Revenue management

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FASTERIVA: UPDATE RULES FOR INDEPENDENT VECTOR ANALYSIS BASED ON NEGENTROPY AND THE MAJORIZE-MINIMIZE PRINCIPLE

FASTERIVA: UPDATE RULES FOR INDEPENDENT VECTOR ANALYSIS BASE...

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IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)

作者： Brendel, Andreas Kellermann, Walter Friedrich Alexander Univ Erlangen Numberg Multimedia Commun & Signal Proc Cauerstr 7 D-91058 Erlangen Germany

ISBN: (纸本)9781665448703

algorithms for Blind Source Separation (BSS) of acoustic signals require efficient and fast converging optimization strategies to adapt to nonstationary signal statistics and time-varying acoustic scenarios. In this paper, we derive fast converging update rules from a negentropy perspective, which are based on the Majorize-Minimize (mm) principle and eigenvalue decomposition. The presented update rules are shown to outperform competing state-of-the-art methods in terms of convergence speed at a comparable runtime due to the restriction to unitary demixing matrices. This is demonstrated by experiments with recorded real-world data.

关键词： Independent Vector Analysis fast convergence mm algorithm FastIVA

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ACCELERATING AUXILIARY FUNCTION-BASED INDEPENDENT VECTOR ANALYSIS

ACCELERATING AUXILIARY FUNCTION-BASED INDEPENDENT VECTOR ANA...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Brendel, Andreas Kellermann, Walter Friedrich Alexander Univ Erlangen Nurnberg Multimedia Commun & Signal Proc Cauerstr 7 D-91058 Erlangen Germany

ISBN: (纸本)9781728176055

Independent Vector Analysis (IVA) is an effective approach for Blind Source Separation (BSS) of convolutive mixtures of audio signals. As a practical realization of an IVA-based BSS algorithm, the so-called AuxIVA update rules based on the Majorize-Minimize (mm) principle have been proposed which allow for fast and computationally efficient optimization of the IVA cost function. For many real-time applications, however, update rules for IVA exhibiting even faster convergence are highly desirable. To this end, we investigate techniques which accelerate the convergence of the AuxIVA update rules without extra computational cost. The efficacy of the proposed methods is verified in experiments representing real-world acoustic scenarios.

关键词： Independent Vector Analysis mm algorithm Convergence Acceleration

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L_p minimisation in sparse array beamforming using semidefinite relaxation

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International Journal of Electronics Letters 2024年第2期12卷 193-209页

作者： Agarwal, Kanika Rai, Chandra Shekhar Yadav, Rajni University School of Information & Communication Technology Guru Gobind Singh Indraprastha University Delhi Dwarka India Department of Electronics & Communication Engineering The Maharaja Agrasen Institute of Technology Guru Gobind Singh Indraprastha University Delhi India

The paper considers the design of sparse arrays in the interference active environment to minimise the system complexity and achieve reduced hardware cost. For this, we propose a sparse array design methodology to attain maximum signal-to-interference plus noise ratio (MaxSINR) in the presence of interfering signals. We formulate the optimisation problem as a real-valued quadratically constrained quadratic program (QCQP) with the non-convex (Formula presented.) norm to promote sparsity, which is iteratively controlled in the proposed approach. We employ the semidefinite relaxation (SDR) technique and the principle of the majorization-minimisation (mm) algorithm to solve the non-convex QCQP problem. The efficacy of the proposed algorithm is demonstrated through the simulation results. The sparse array obtained through the proposed method performs well when compared with the reweighted (Formula presented.) algorithm. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Adaptive beamforming mm algorithm QCQP reweighted ℓ1-norm SDR Signal-to-interference-plus-noise ratio (SINR) sparse array ℓp-minimisation

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Deep Learning-Assisted Beamforming Design and BER Evaluation in Multi-User Downlink Systems 12

Deep Learning-Assisted Beamforming Design and BER Evaluation...

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12th International Conference on Ubiquitous and Future Networks (ICUFN)

作者： Kim, Junbeom Lee, Hoon Hong, Seung-Eun Park, Seok-Hwan Jeonbuk Natl Univ Div Elect Engn Jeonju 54896 South Korea Pukyong Natl Univ Dept Informat & Commun Engn Busan 48513 South Korea Elect & Telecommun Res Inst ETRI Daejeon 34129 South Korea

ISBN: (纸本)9781728164762

This paper studies deep learning-based beamforming design schemes for multi-user downlink systems. Two distinct objectives are considered: sum-rate maximization and min-rate maximization. Each of formulations is first tackled by classical majorization-minimization (mm) algorithms that find a locally optimum point iteratively. To reduce computational overheads of the mm algorithms, deep neural networks (DNNs) are introduced which yield optimized beamforming solutions from channel vector inputs. Performance of trained DNNs is evaluated in terms of bit-error rate (BER) measure. Numerical results show that deep learning approaches achieve the BER performance very close to mm algorithms with much reduced complexity. Also, it is desirable to adopt the minimum-rate criterion to achieve low BER performance rather than sum-rate.

关键词： Deep learning beamforming mm algorithm

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Distributed learning of finite Gaussian mixtures

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 4265-4304页

作者： Qiong Zhang Jiahua Chen Department of Statistics University of British Columbia Vancouver Canada

Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining statistical validity and efficiency. In this situation, the split-and-conquer strategy is among the most effective solutions to many statistical problems, including quantile processes, regression analysis, principal eigenspaces, and exponential families. This paper applies this strategy to develop a distributed learning procedure of finite Gaussian mixtures. We recommend a reduction strategy and invent an effective majorization-minimization algorithm. The new estimator is consistent and retains root-n consistency under some general conditions. Experiments based on simulated and real-world datasets show that the proposed estimator has comparable statistical performance with the global estimator based on the full dataset, if the latter is feasible. It can even outperform the global estimator for the purpose of clustering if the model assumption does not fully match the real-world data. It also has better statistical and computational performance than some existing split-and-conquer approaches.

关键词： Barycenter Gaussian mixture global convergence mixture reduction mm algorithm model-based clustering split-and-conquer

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Generalized case-cohort analysis for constrained estimation in the Cox's model

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COmmUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第1期49卷 45-65页

作者： Pan, Yingli Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China

The generalized case-cohort sampling is a best choice to reduce study cost and time, which contains many sampling steps, each step takes a random sample of a certain size without replacement from a certain subset of the cohort, the number of steps, the choice of sample size and the sampling subset must not use the information about the observed covariates. The constrained estimation in the Cox's model for the right-censored survival data has been studied by Ding, Tian, and Kam, who proposed a novel minorization-maximization (mm) algorithm for the constrained estimation. In this paper, we derive an estimating equation by a sample reuse and local average weight method based on generalized case-cohort data and generalize the mm algorithm to get the constrained estimator in the Cox's model with parameter subject to box or linear inequality constraint. Asymptotic properties are presented. The small sample operating characteristics of the proposed method are examined via simulation studies and are illustrated on a dataset from Wilms tumor studies.

关键词： Constrained estimation Cox's model generalized case-cohort sampling mm algorithm

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