Asymptotic Efficiency Research Articles

Volatility estimation of hidden Markov processes and adaptive filtration

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. The coefficients of this system are supposed to depend on some unknown parameter. The problem of estimation of these parameters is considered and the possibility of the approximation of the filtering equations is discussed. An estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of method of moments estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this method of moments estimator and Fisher-score device allow us to introduce the One-step MLE-process and adaptive Kalman–Bucy filter. The asymptotic efficiency of the proposed filter is discussed.

Efficient inference of parent-of-origin effect using case-control mother-child genotype data

Parent-of-origin effect plays an important role in mammal development and disorder. Case-control mother-child pair genotype data can be used to detect parent-of-origin effect and is often convenient to collect in practice. Most existing methods for assessing parent-of-origin effect do not incorporate any covariates, which may be required to control for confounding factors. We propose to model the parent-of-origin effect through a logistic regression model, with predictors including maternal and child genotypes, parental origins, and covariates. The parental origins may not be fully inferred from genotypes of a target genetic marker, so we propose to use genotypes of markers tightly linked to the target marker to increase inference efficiency. A robust statistical inference procedure is developed based on a modified profile log-likelihood in a retrospective way. A computationally feasible expectation–maximization algorithm is devised to estimate all unknown parameters involved in the modified profile log-likelihood. This algorithm differs from the conventional expectation–maximization algorithm in the sense that it is based on a modified instead of the original profile log-likelihood function. The convergence of the algorithm is established under some mild regularity conditions. This expectation–maximization algorithm also allows convenient handling of missing child genotypes. Large sample properties, including weak consistency, asymptotic normality, and asymptotic efficiency, are established for the proposed estimator under some mild regularity conditions. Finite sample properties are evaluated through extensive simulation studies and the application to a real dataset.

EXPRESS: Sharing the Shared Rides: Multi-party Carpooling Supported Strategy-Proof Double Auctions

Multi-party carpooling emerges as a burgeoning shared transportation scheme whereby the trip shared by each driver is shared among multi-party riders whose itineraries coincide. Confronting the information asymmetry and the voluntary self-interested nature of bilateral participants in matching and pricing operations, this study designs Multiparty cArpooling SupporTed stratEgy-pRoof (MASTER) double auction mechanisms considering personalized carpooling constraints. First, in a scheduled carpooling scenario, two MASTERS mechanisms that masterfully blend the ideas of the famed trade reduction method and multi-stage approach are proposed which implement distinct group bid determination approaches for responding to different market conditions. Second, in an on-demand carpooling scenario, two parameterized MASTERO mechanisms that integrate frustration-based promotion to proactively prioritize matching and deferentially compensate riders based on their waits are contrived which also endow the platform with operational flexibility to agilely pursue alterable operational objectives by adjusting promotion strength. We prove theoretically that the proposed mechanisms satisfy strategy proofness (SP), budget balance (BB), individual rationality (IR), and asymptotic efficiency (AsE) under mild conditions. Experimental results reveal that multi-party carpooling constitutes a multi-win solution under higher rider-driver ratios whilst it could be detrimental to drivers otherwise, which can be ameliorated by favoring the driver side in determining promotion strength. Simulation studies manifest that our proposed auction mechanisms could bring benefits concerning allocation efficiency and service responsiveness compared with their academic and practical counterparts.We also shed light on choosing among alternative mechanisms according to market conditions and operational orientations.

Randomised controlled, patient-blinded, multicentre, superiority trial to evaluate the efficacy of the line-attached sheath-type traction device for endoscopic submucosal dissection in patients with superficial gastric neoplasms

IntroductionEndoTrac is a line-attached sheath-type traction device that enables us to control the direction and the force of traction during endoscopic submucosal dissection (ESD). The efficacy of EndoTrac for gastric...

Asymptotic Relative Efficiency Comparison for some Fit Indices in Structural Equation Modeling

There are many fit statistics used in the structural equation modeling, and new ones are consistently being developed. Because of the variety of fit statistics, it is very important to be able to decide which fit statistics are appropriate to use in studies. When comparing any two statistics, the asymptotic relative efficiency (ARE) between them is used. The ARE can use as a power of the fit indices is one of the familiar optimal criteria. It is frequently more convenient, and also more suggestive, to use a measure of relative merit called the relative efficiency. This study aimed to compare of fit indices using Fraser’s asymptotic relative efficiency. The data sets were derived from the multivariate normal distribution using the mean vector and covariance matrix. It was determined that the most efficient fit indices in terms of asymptotic relative efficiency were Z-Test of Wilson & Hilferty (W&H), Root Mean Square Error of Approximation (RMSEA), and Chi-Square indices, respectively.

Covariate adjustment in randomized experiments with missing outcomes and covariates

Summary Covariate adjustment can improve precision in analysing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis. When some outcomes are missing, we consider combining these two adjustment methods with inverse probability of observation weighting for handling missing outcomes, and show that the equivalence between the two methods breaks down. Regression adjustment no longer ensures efficiency gain over unadjusted analysis unless the true outcome model is linear in covariates or the outcomes are missing completely at random. Propensity score weighting, in contrast, still guarantees efficiency over unadjusted analysis, and including more covariates in adjustment never harms asymptotic efficiency. Moreover, we establish the value of using partially observed covariates to secure additional efficiency by the missingness indicator method, which imputes all missing covariates by zero and uses the union of the completed covariates and corresponding missingness indicators as the new, fully observed covariates. Based on these findings, we recommend using regression adjustment in combination with the missingness indicator method if the linear outcome model or missing complete at random assumption is plausible and using propensity score weighting with the missingness indicator method otherwise.

Minimum density power divergence estimation for the generalized exponential distribution

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001a). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

No star is good news: A unified look at rerandomization based on [formula omitted]-values from covariate balance tests

Randomized experiments balance all covariates on average and are considered the gold standard for estimating treatment effects. Chance imbalances are nonetheless common in realized treatment allocations. To inform readers of the comparability of treatment groups at baseline, contemporary scientific publications often report covariate balance tables with not only covariate means by treatment group but also the associated p-values from significance tests of their differences. The practical need to avoid small p-values as indicators of poor balance motivates balance check and rerandomization based on these p-values from covariate balance tests (ReP) as an attractive tool for improving covariate balance in designing randomized experiments. Despite the intuitiveness of such strategy and its possibly already widespread use in practice, the literature lacks results about its implications on subsequent inference, subjecting many effectively rerandomized experiments to possibly inefficient analyses. To fill this gap, we examine a variety of potentially useful schemes for ReP and quantify their impact on subsequent inference. Specifically, we focus on three estimators of the average treatment effect from the unadjusted, additive, and interacted linear regressions of the outcome on treatment, respectively, and derive their asymptotic sampling properties under ReP. The main findings are threefold. First, the estimator from the interacted regression is asymptotically the most efficient under all ReP schemes examined, and permits convenient regression-assisted inference identical to that under complete randomization. Second, ReP, in contrast to complete randomization, improves the asymptotic efficiency of the estimators from the unadjusted and additive regressions. Standard regression analyses are accordingly still valid but in general overconservative. Third, ReP reduces the asymptotic conditional biases of the three estimators and improves their coherence in terms of mean squared difference. These results establish ReP as a convenient tool for improving covariate balance in designing randomized experiments, and we recommend using the interacted regression for analyzing data from ReP designs.

Advancements in Laplace transform techniques: Performing non-parametric hypothesis testing on real-world data through statistical analysis

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test’s statistical power and explores Pitman’s asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios.

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

This study deals with a novel category of life distributions called the new better than renewal used in moment generating function (NBRUmgf) class. It delves into the connections between this form of aging and established aging categories, along with its relevance in a shock model. Additionally, it explores how this aging concept remains consistent through certain reliability operations which is consider a very important tool in reliability engineering. The research computes Pitman's asymptotic efficiencies for this testing procedure, comparing them with alternative methods. Furthermore, the study furnishes a comprehensive table of percentiles for the test statistic associated with this proposed method. Furthermore, in order to showcase the relevance of the study's conclusions, we utilize distinct real-world datasets, which illustrate the effectiveness of our test across various types of real data.

RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS.

To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's , Blum-Kiefer-Rosenblatt's and Bergsma-Dassios-Yanagimoto's . Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the asymptotic efficiency of the proposed tests based on and are sorted in a descending order.

Bayesian Regression Analysis using Median Rank Set Sampling

Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.

The effect of the working correlation on fitting models to longitudinal data

AbstractWe present a detailed discussion of the theoretical properties of quadratic inference function estimators of the parameters in marginal linear regression models. We consider the effect of the choice of working correlation on fundamental questions including the existence of quadratic inference function estimators, their relationship with generalized estimating equations estimators, and the robustness and asymptotic relative efficiency of quadratic inference function and generalized estimating equations estimators. We show that the quadratic inference function estimators do not always exist and propose a way to handle this. We then show that they have unbounded influence functions and can be more or less asymptotically efficient than generalized estimating equations estimators. We also present empirical evidence to demonstrate these results. We conclude that the choice of working correlation can have surprisingly large effects.

Improved maximum likelihood estimators of the parameters of the log-exponential power distribution with applications

Owing that ensuring true representative samples from a population is dependent on sampling via sample estimators, in this paper, we established the sample maximum likelihood (ML) estimators of the location (μ), scale (σ2) and shape (β) parameters of Log-Exponential Power Distribution (LEPD), under simple random sampling (SRS), ranked set sampling (RSS) and another introduced sampling called general RSS (GRSS). The study then obtained the Fisher information (FI) of the obtained estimators under different cases: when one parameter, two parameters and when all the parameters are unknown, for each of the sampling procedure and compute its asymptotic relative efficiency (RE). The FI estimate, when GRSS samples are obtained from ith or (ith,jth) ordered samples, were established along with its RE. Application from simulated and real life data with imperfect units ranking was used to demonstrate the relevance of the study, in terms of sampling efficiency within the shortest length of interval estimate. Application of GRSS to the Food and Agricultural Organization (FAO) projected data on cattle meat boom by 2050 was considered, the implication of the sudden increase in cattle population in Nigeria and the recommendation to prevent subsequent crises due to competition for land among farmers, herders and other populace was analytically established. Finally, the procedure was used to establish the cause of increased suicide rate in Nigeria has recently published by World Health Organization (WHO).

Speedup and efficiency of computational parallelization: A unifying approach and asymptotic analysis

In high performance computing environments, we observe an ongoing increase in the available number of cores. For example, the current TOP500 list reveals that nine clusters have more than 1 million cores. This development calls for re-emphasizing performance (scalability) analysis and speedup laws as suggested in the literature (e.g., Amdahl's law and Gustafson's law), with a focus on asymptotic performance. Understanding speedup and efficiency issues of algorithmic parallelism is useful for several purposes, including the optimization of system operations, temporal predictions on the execution of a program, the analysis of asymptotic properties, and the determination of speedup bounds. However, the literature is fragmented and shows a large diversity and heterogeneity of speedup models and laws. These phenomena make it challenging to obtain an overview of the models and their relationships, to identify the determinants of performance in a given algorithmic and computational context, and, finally, to determine the applicability of performance models and laws to a particular parallel computing setting. In this work, I provide a generic speedup (and thus also efficiency) model for homogeneous computing environments. My approach generalizes many prominent models suggested in the literature and allows showing that they can be considered special cases of a unifying approach. The genericity of the unifying speedup model is achieved through parameterization. Considering combinations of parameter ranges, I identify six different asymptotic speedup cases and eight different asymptotic efficiency cases. Jointly applying these speedup and efficiency cases, I derive eleven scalability cases, from which I build a scalability typology. Researchers can draw upon my suggested typology to classify their speedup model and to determine the asymptotic behavior when the number of parallel processing units increases. Also, the description of two computational experiments demonstrates the practical application of the model and the typology. In addition, my results may be used and extended in future research to address various extensions of my setting.

Nonparametric E-tests of Symmetry

The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman’s asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.

Convergence Analysis of Mean Shift.

The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly mild conditions, with the help of the argument concerning the Łojasiewicz inequality. Our findings extend existing ones covering analytic kernels and the Epanechnikov kernel. Those are significant in that they cover the biweight kernel, which is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.

Quasi-maximum Likelihood Inference for Linear Double Autoregressive Models

This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only fractional moment of the observed process. We propose a Gaussian quasi-maximum likelihood estimator (G-QMLE) and an exponential quasi-maximum likelihood estimator (E-QMLE) for the linear DAR model, and establish the consistency and asymptotic normality for both estimators. Based on the G-QMLE and E-QMLE, two Bayesian information criteria are proposed for model selection, and two mixed portmanteau tests are constructed to check the adequacy of fitted models. Moreover, we compare the proposed G-QMLE and E-QMLE with the existing doubly weighted quantile regression estimator in terms of the asymptotic efficiency and numerical performance. Simulation studies illustrate the finite-sample performance of the proposed inference tools, and a real example on the Bitcoin return series shows the usefulness of the proposed inference tools.

Vecchia Likelihood Approximation for Accurate and Fast Inference with Intractable Spatial Max-Stable Models

Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima. However, likelihood inference for such models suffers severely from the curse of dimensionality, since the likelihood function involves a combinatorially exploding number of terms. In this article, we propose using the Vecchia approximation, which conveniently decomposes the full joint density into a linear number of low-dimensional conditional density terms based on well-chosen conditioning sets designed to improve and accelerate inference in high dimensions. Theoretical asymptotic relative efficiencies in the Gaussian setting and simulation experiments in the max-stable setting show significant efficiency gains and computational savings using the Vecchia likelihood approximation method compared to traditional composite likelihoods. Our application to extreme sea surface temperature data at more than a thousand sites across the entire Red Sea further demonstrates the superiority of the Vecchia likelihood approximation for fitting complex models with intractable likelihoods, delivering significantly better results than traditional composite likelihoods, and accurately capturing the extremal dependence structure at lower computational cost. Supplementary materials for this article are available online.

Penalised estimation of partially linear additive zero-inflated Bernoulli regression models

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. ‘Semiparametric Zero-Inflated Bernoulli Regression with Applications’, Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study.