Asymptotic Relative Efficiency Research Articles

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.

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.

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).

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.

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.

Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators

The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency (ARE) of the Kaplan–Meier survival estimator compared to parametric survival estimators. We begin by generalizing Miller’s approach and presenting a formula that enables the estimation (numerical or exact) of ARE for various survival distributions and types of censoring. We examine the effect of follow-up time and censoring on ARE. The article concludes with a discussion about the reasons behind the lower and time-dependent ARE of the Kaplan–Meier survival estimator.

A new non-parametric hypothesis testing with reliability analysis applications to model some real data

Due to the essential necessities of current technology and contemporary sciences, a methodical approach to investigating every occurrence or action occurring in the world was required. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products. In actuality, there are instances when system parts gradually deteriorate over time t, at which point the system needs to be updated by replacing the spare parts. Although renewal tries to improve system usability, it is unable to restore the system to its prior state. We discovered that an entirely novel domain of reliability known as classes of life distributions has emerged as a result of the growth of criteria for determining the success or failure of dependability over the previous few decades. Moreover, the other nonparametric tests of life distribution lack test efficiency and have low test power. On the other hand, based on that approach, the non-parametric statistical test utilized in this study evaluates different types of treatment by examining failure behavior in the survival data that was collected. As a result, in this ivestigation, we have developed a novel test of life distribution in this study that considers the power and effectiveness of the test. In order to compare data belonging to the harmonic new better than used in expectation (HNBUE) class with data that follow an exponential distribution, this article suggests nonparametric tests for both censored and uncensored data. The higher percentile points of the test statistics are collected, and the suggested test's normality is verified. The Pitman asymptotic relative efficiency (PARE) and powers of proposed test are calculated a few well-known alternative asymmetric models. Three asymmetric real-world data sets are examined to demonstrate the paper's findings.

Determining the late effect parameter in the Fleming-Harrington test using asymptotic relative efficiency in cancer immunotherapy clinical trials

ABSTRACT The delayed treatment effect, which manifests as a separation of survival curves after a change point, has often been observed in immunotherapy clinical trials. A late effect of this kind may violate the proportional hazards assumption, resulting in the non-negligible loss of statistical power of an ordinary log-rank test when comparing survival curves. The Fleming-Harrington (FH) test, a weighted log-rank test, is configured to mitigate the loss of power by incorporating a weight function with two parameters, one each for early and late treatment effects. The two parameters need to be appropriately determined, but no helpful guides have been fully established. Since the late effect is expected in immunotherapy trials, we focus on the late effect parameter in this study. We consider parameterizing the late effect in a readily interpretable fashion and determining the optimal late effect parameter in the FH test to maintain statistical power in reference to the asymptotic relative efficiency (ARE). The optimization is carried out under three lag models (i.e. linear, threshold, and generalized linear lag), where the optimal weights are proportional to the lag functions characterized by the change points. Extensive simulation studies showed that the FH test with the selected late parameter reliably provided sufficient power even when the change points in the lag models were misspecified. This finding suggests that the FH test with the ARE-guided late parameter may be a reasonable and practical choice for the primary analysis in immunotherapy clinical trials.

Asymptotic properties of Spearman’s footrule and Gini’s gamma in bivariate normal model

This paper aims at rejuvenating the two rank correlation coefficients, Spearman’s footrule (SF) and Gini’s gamma (GG), which were forgotten in the literature for a long time due to lack of knowledge concerning their statistical properties. Under the common bivariate normal model, we establish the asymptotic analytical expressions of the mean and variance of SF and GG, and investigate the performances of SF and GG from the aspects of biased effect, approximate variance and asymptotic relative efficiency (ARE). Moreover, we further study the robustness of SF and GG under contaminated normal models. In order to get a deeper understanding of their performances, we also compare SF and GG with Kendall’s tau (KT) and Spearman’s rho (SR), the most widely used rank correlation coefficients, in terms of bias and mean square error (MSE) under both the normal and contaminated normal models. Finally we show an application of SF and GG in the field of signal processing through the example of time-delay estimation. Simulation results indicate that SF and GG outperform SR and KT in some cases. The new findings discovered in this paper enable SF and GG to play complementary roles to KT and SR in practice.

Asymptotic Relative Efficiency of the Kendall and Spearman Correlation Statistics

A necessary and sufficient condition for Pitman's asymptotic relative efficiency of the Kendall and Spearman correlation statistics for the independence test to be $1$ is given, in terms of certain smoothness and nondegeneracy properties of the model. Corresponding easy-to-use and broadly applicable sufficient conditions are obtained. These conditions hold for most well-known models of dependence.

Two Sample Statistical Test for Location Parameters

A class of distribution-free tests for the homogeneity of location parameters is proposed and compared with different competitors in terms of Pitman asymptotic relative efficiency. A numerical example is provided and a simulation study is made to check the performance of the tests.

Algorithm 1034: An Accelerated Algorithm to Compute the Q n Robust Statistic, with Corrections to Constants

The robust scale estimator Q n developed by Croux and Rousseeuw [ 3 ], for the computation of which they provided a deterministic algorithm, has proven to be very useful in several domains including in quality management and time series analysis. It has interesting mathematical (50% breakdown, 82% Asymptotic Relative Efficiency) and computing ( O(nlogn) time, O ( n ) space) properties. While working on a faster algorithm to compute Q n , we have discovered an error in the computation of the d constant, and as a consequence in the d n constants that are used to scale the statistic for consistency with the variance of a normal sample. These errors have been reproduced in several articles including in the International Standard Organisation 13,528 [ 12 ] document. In this article, we fix the errors and present a new approach, which includes a new algorithm, allowing computations to run 1.3 to 4.5 times faster when n grows from 10 to 100,000.

Robust testing procedures for scale differences in paired data

Several statistical tests have been proposed in the literature to assess the difference between two scale parameters in paired data. If the location parameters of each sample are different, many of these test statistics are adjusted using the estimated location parameters. Then, the performance of the test statistics depends on the selection of the location estimators. In this study, the asymptotically distribution-free test based on the U-statistic, which does not depend on two location parameters, is constructed. The asymptotic normality and the asymptotic power of the proposed test are examined. Furthermore, the proposed test is compared with the existing tests in terms of Pitman's asymptotic relative efficiency. To improve the Type I error rate in the small sample size, the robust test procedure based on the percentile bootstrap is also proposed. Our simulation studies show that the Type I error rate of the proposed test is more controlled and robust than existing tests in many situations. Further, the empirical power of the proposed test is shown to be high for heavy-tailed or asymmetric distributions.

On the Robust Estimation of Spatial Autoregressive Models

The spatial autoregressive (SAR) model is commonly used for cross-sectional data with spatial dependence in the response variable. A robust M-estimator for the SAR model with independent normal random errors is proposed, which is resistant to extreme contamination or outliers in the data. The proposed estimator is defined by a set of robust estimating functions derived by modifying the estimating functions for the standard maximum likelihood (ML) estimator using the Huber function. An iterative algorithm based on iteratively reweighted least squares and a fixed point method is provided to compute the robust M-estimator. The proposed estimator is shown to be Fisher-consistent under the core model, has a bounded influence function, and is asymptotically normally distributed. A closed-form expression for the asymptotic covariance matrix estimator under the core model is derived, and used to study the asymptotic relative efficiency of the proposed estimator. Simulation studies demonstrate that the proposed robust M-estimator greatly outperforms the ML estimator as well as several other non-robust estimators of the SAR model, in terms of both estimation and inference under different contamination scenarios. Additionally, the proposed estimator offers comparable performance to some robust estimators of the SAR model under contamination. Applying the robust M-estimator for the SAR model to the U.S. federal grants and U.S. Nielsen Local Television View datasets reveals strong positive spatial dependence in the grant value among counties, insignificant positive effect of news watching on grant distribution, and evidence of outliers in the data. This results in different conclusions from those obtained using the ML estimator.

Asymptotic relative efficiency of the Kendall and Spearman correlation statistics

Необходимое и достаточное условие для того, чтобы асимптотическая относительная эффективность Питмена для корреляционных статистик Кендалла и Спирмена для критерия независимости равнялась $1$, дано в терминах некоторых свойств гладкости и невырожденности модели. Получены соответствующие простые в использовании и широко применимые достаточные условия. Эти условия выполняются для большинства известных моделей зависимости.

Composite smoothed quantile regression

Composite quantile regression (CQR) is an efficient method to estimate parameters of the linear model with non‐Gaussian random noise. The non‐smoothness of CQR loss prevents many efficient algorithms from being used. In this paper, we propose the composite smoothed quantile regression (CSQR) model and investigate the inference problem for a large‐scale dataset, in which the dimensionality is allowed to increase with the sample size while . After applying the convolution smoothing technique to the composite quantile loss, we obtain the convex and twice differentiable CSQR loss function, which can be optimized via the gradient descent algorithm. Theoretically, we establish the non‐asymptotic error bound for the CSQR estimators and further provide the Bahadur representation and the Berry–Esseen bound, from which the asymptotic normality of CSQR estimator can be immediately derived. To make valid inference, we construct the confidence intervals that based on the asymptotic distribution. Besides, we also explore the asymptotic relative efficiency of the CSQR estimator with respect to the standard CQR estimator. At last, we provide extensive numerical experiments on both simulated and real data to demonstrate the good performance of our CSQR estimator compared with some baselines.

Conjuring Power from a Theory of Change: The PWRD Method for Trials with Anticipated Variation in Effects

We present an aggregation scheme that increases power in randomized controlled trials and quasi-experiments when the intervention possesses a robust and well-articulated theory of change. Intervention studies using longitudinal data often include multiple observations on individuals, some of which may be more likely to manifest a treatment effect than others. An intervention’s theory of change provides guidance as to which of those observations are best situated to exhibit that treatment effect. Our power-maximizing weighting for repeated-measurements with delayed-effects scheme, PWRD aggregation, converts the theory of change into a test statistic with improved asymptotic relative efficiency, delivering tests with greater statistical power. We illustrate this method on an IES-funded cluster randomized trial testing the efficacy of a reading intervention designed to assist early elementary students at risk of falling behind their peers. The salient theory of change holds program benefits to be delayed and non-uniform, experienced after a student’s performance stalls. In this instance, the PWRD technique’s effect on power is found to be comparable to that of doubling the number of clusters in the experiment.