Search

In this study, the stress-strength reliability, R = P(Y < X) where Y represents the stress of a component and X represents this component’s strength, is obtained when X and Y have two independents generalized Gompertz distribution with different shape parameters under progressive type-II censoring. The Bayes and maximum likelihood estimators of stress-strength reliability can not be acquired in closed forms. The approximate Bayes estimators under squared error loss function by using Lindley’s approximations for stressstrength reliability are derived. A Monte Carlo simulation study is done to check performances of the approximate Bayes against performances of maximum likelihood estimators and observe the coverage probabilities and the intervals’ average width. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Two applications based on real datasets are provided.

Let $V$ be a countably generated right vector space over a field $F$ and $\sigma\in End(V_F )$ be a shift operator. We show that there exist a unit $u$ and an idempotent $e$ such that $1-u,\sigma-u$ are units in $End(V_F)$ and $1-e,\sigma-e$ are idempotents in $End(V_F)$. We also obtain that if $D$ is a division ring and $D\ncong \mathbb Z_2, \mathbb Z_3 $, then $1-u,\alpha-u$ are units in $End(V_D)$ for any $\alpha\in End(V_D)$.

This paper is concerned with the study of stability analysis to a complicated recovered fracturing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction-diffusion equation with Neumann boundary conditions. Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation. Then, we prove that the existence of solutions to perturbated problems and the solution sequence to perturbated problems are uniformly bounded. Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.

The Moore and Bilikam family includes lifetime distributions, hence there is a need for a meticulous investigation of the proposed family. We evaluate different estimation procedures for both parameters and reliability function of the Moore and Bilikam family comprehensively, including the maximum likelihood, Bayesian and E-Bayesian estimation methods. The estimation methods of the Moore and Bilikam family are compared via the simulation data, whereas simulation results of the Burr XII sub-model are reported. Based on the simulation approach, we concluded the estimates of the Moore and Bilikam family are convergent to the corresponding parameters, and the root mean square error values derived by the E-Bayesian method are less than other estimators. The analysis of the time between failures of secondary reactor pumps data set has been represented for illustrative purposes, which confirmed simulation results.

An important bias can occur when estimating coefficients by maximizing the known partial likelihood function in the Cox regression model with the measurement error covariate. We focus here on Bayesian methods in order to adjust measurement error and aim to propose an adjusting Bayesian method. Constructing simulation studies using Markov Chain Monte Carlo simulation techniques to investigate the performance of models. We compare the proposed method with the existing method that used partial likelihood function, Bayesian Cox regression model ignoring measurement error, the adjusted Bayesian Cox regression model that exists in the literature by a simulation study which consists of different sample sizes, censoring rates, reliability levels, and regression coefficients. Simulation studies indicate that the proposed method outperformed others given some scenarios. A real data set is analyzed for an illustration of the findings.

Recently‎, ‎the beta regression model has been used in several fields of science to model data in the form of rate or proportion‎. ‎In this paper‎, ‎we propose some novel and improved methods to estimate parameters in the beta regression model‎. ‎We consider a sub-space on the regression coefficients of the beta regression model and combine the unrestricted and restricted estimators then we present Stein-type and preliminary estimators‎. ‎We develop the expressions for the proposed estimators' asymptotic biases and their quadratic risks‎. ‎Numerical studies through Monte Carlo simulations are used to evaluate the performance of the proposed estimators in terms of their simulated relative efficiency‎. ‎The results show that the proposed estimators outperform the unrestricted estimator when the restrictions hold‎. ‎Finally‎, ‎an empirical application is provided to demonstrate the practical usefulness of the proposed ‎estimators.‎

This article presents two approaches to extend classical MANOVA tests to the unequal covariances case. The first approach is illustrated by extending the classical Wilks test, which is valid only when covariances are equal. Such tests will be based on exact probabilities of certain extreme regions. We will also show how tests numerically equivalent to the parametric bootstrap tests could be easily obtained without using any bootstrap sampling arguments, so that resulting p-values are also based on exact probabilities of well defined extreme regions. Being systematic approaches, by taking similar approaches, re- searchers should be able to derive generalized tests in MANCOVA, higher-way MANOVA, and in RM MANOVA under heteroscedasticity, in which the parametric bootstrap type approaches run into difficulties.

The cause-specific hazard function plays an important role in developing the regression models for competing risks survival data. Proportional hazards and additive hazards are the commonly used regression approaches in survival analysis. Mostly, in literature, the proportional hazards model was used for parametric regression modelling of survival data. In this article, we introduce a parametric additive hazards regression model for survival analysis with competing risks. For employing a parametric model we consider the modified Weibull distribution as a baseline model which is capable to model survival data with non-monotonic behaviour of hazard rate. The estimation process is carried out via maximum likelihood and Bayesian approaches. In addition to Bayesian methods, a class of non-informative types of prior is introduced with squared error (symmetric) and linear-exponential (asymmetric) loss functions. The relative performance of the different estimators is assessed using Monte Carlo simulation. Finally, using the proposed methodology, a real data analysis is performed.

Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation (ABC) is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC (Population Monte Carlo, PMC) with a Conditional Density Estimation (CDE) approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

The increase of the product variety in the financial markets requires a clear understanding of the dependence between such instruments for the decision-makers. For a few decades, such dependence structures were often modeled with symmetric copula families. However, financial data may reveal an asymmetric structure, which can be determined via directional dependence measures in the context of copulas. Previously, some asymmetric copula models were proposed in different ways using Khoudraji’s device. But they are merely used for financial time series data in a broader sense. In this study, a new set of asymmetric copulas were defined by using one parameter of Archimedean copula families. For this aim, widely used copula families were studied and the corresponding directional dependence measures were analyzed. To illustrate the efficiency of the parameter estimation method, a small simulation scenario consisting of an asymmetric dependence pattern was carried out. Thereafter, the proposed asymmetric bi-variate copulas with directional dependence coefficients were investigated for two different stock market data. The study’s primary findings suggested that the newly generated asymmetric models might be useful for directional dependence. Especially, the estimated directional dependence coefficients can serve as an indicator to explain the variability of one stock in terms of the other.

Characterizing the wind speed distribution properly is essential for the satisfactory production of potential energy in wind farms, being the mixture models usually employed in the description of such data. However, some mixture models commonly have the undesirable property of non-identifiability. In this work, we present an alternative distribution which is able to fit the wind speed data decently. The new model, called Normal-Weibull-Weibull, is identifiable and its cumulative distribution function is written as a composition of two baseline functions. We discuss structural properties of the class that generates the proposed model, such as the linear representation of the probability density function, moments and moment generating function. We perform a Monte Carlo simulation study to investigate the behavior of the maximum likelihood estimates of the parameters. Finally, we present applications of the new distribution for modelling wind speed data measured in five different cities of the Northeastern Region of Brazil.

Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as $O(\log(n)/n)$ (resp. $O(1/n)$). Assuming posterior recovery, one may interpret credible sets (resp. enlarged credible sets) as asymptotically consistent confidence sets; the diameters of those credible sets are controlled by the rate of posterior concentration. If credible levels are chosen to grow to one quickly enough, corresponding credible sets can be interpreted as frequentist confidence sets without conditions on posterior concentration. In the regimes with $O(1/n)$ edge sparsity, or when within-community and between-community edge probabilities are very close, credible sets may be enlarged to achieve frequentist asymptotic coverage, also without conditions on posterior concentration., 29 pp., 3 fig

We investigate the value of a two-armed Bayesian response adaptive randomization (RAR) design to investigate early preterm birth rates of high versus low dose of docosahexaenoic acid during pregnancy. Unexpectedly, the COVID-19 pandemic forced recruitment to pause at 1100 participants rather than the planned 1355. The difference in power between number of participants at the pause and planned was 87% and 90% respectively. We decided to stop the study. This paper describes how the RAR was used to execute the study. The value of RAR in two-armed studies is quite high and their use in the future is promising.

There is increasing interest in detecting collective anomalies: potentially short periods of time where the features of data change before reverting back to normal behaviour. We propose a new method for detecting a collective anomaly in VAR models. Our focus is on situations where the change in the VAR coefficient matrix at an anomaly is sparse, i.e. a small number of entries of the VAR coefficient matrix change. To tackle this problem, we propose a test statistic for a local segment that is built on the lasso estimator of the change in model parameters. This enables us to detect a sparse change more efficiently and our lasso-based approach becomes especially advantageous when the anomalous interval is short. We show that the new procedure controls Type 1 error and has asymptotic power tending to one. The practicality of our approach is demonstrated through simulations and two data examples, involving New York taxi trip data and EEG data.

Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain bandwidth under the high-dimensional framework. Though several testing methods have been proposed in the literature, the existing tests are only powerful for some alternatives with certain sparsity levels, whereas they may not be powerful for alternatives with other sparsity structures. The goal of this paper is to propose a new test for the bandedness of high-dimensional covariance matrix, which is powerful for alternatives with various sparsity levels. The proposed new test also be used for testing the banded structure of covariance matrices of error vectors in high-dimensional factor models. Based on these statistics, a consistent bandwidth estimator is also introduced for a banded high dimensional covariance matrix. Extensive simulation studies and an application to a prostate cancer dataset from protein mass spectroscopy are conducted for evaluating the effectiveness of the proposed adaptive tests blue and bandwidth estimator for the banded covariance matrix.

We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation systems where a unit corresponds to a spatially distinct sub-population. Metapopulation systems are characterized by strong dependence through time within a single unit and relatively weak interactions between units, and these properties make block particle filters an effective tool for simulation-based likelihood evaluation. Iterated filtering algorithms can facilitate likelihood maximization for simulation-based filters. We introduce an iterated block particle filter applicable when parameters are unit-specific or shared between units. We demonstrate this algorithm by performing inference on a coupled epidemiological model describing spatiotemporal measles case report data for twenty towns.

Survival outcomes are common in comparative effectiveness studies and require unique handling because they are usually incompletely observed due to right-censoring. A ``once for all'' approach for causal inference with survival outcomes constructs pseudo-observations and allows standard methods such as propensity score weighting to proceed as if the outcomes are completely observed. For a general class of model-free causal estimands with survival outcomes on user-specified target populations, we develop corresponding propensity score weighting estimators based on the pseudo-observations and establish their asymptotic properties. In particular, utilizing the functional delta-method and the von Mises expansion, we derive a new closed-form variance of the weighting estimator that takes into account the uncertainty due to both pseudo-observation calculation and propensity score estimation. This allows valid and computationally efficient inference without resampling. We also prove the optimal efficiency property of the overlap weights within the class of balancing weights for survival outcomes. The proposed methods are applicable to both binary and multiple treatments. Extensive simulations are conducted to explore the operating characteristics of the proposed method versus other commonly used alternatives. We apply the proposed method to compare the causal effects of three popular treatment approaches for prostate cancer patients., 40 pages, 2 figures, 1 table

In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often associated with Gaussian processes. However, when considering non-linear prediction for non-Gaussian and categorical data, the Kriging prediction is no longer optimal, and the associated variance is often overly optimistic. Although deep neural networks (DNNs) are widely used for general classification and prediction, they have not been studied thoroughly for data with spatial dependence. In this work, we propose a novel DNN structure for spatial prediction, where the spatial dependence is captured by adding an embedding layer of spatial coordinates with basis functions. We show in theory and simulation studies that the proposed DeepKriging method has a direct link to Kriging in the Gaussian case, and it has multiple advantages over Kriging for non-Gaussian and non-stationary data, i.e., it provides non-linear predictions and thus has smaller approximation errors, it does not require operations on covariance matrices and thus is scalable for large datasets, and with sufficiently many hidden neurons, it provides the optimal prediction in terms of model capacity. We further explore the possibility of quantifying prediction uncertainties based on density prediction without assuming any data distribution. Finally, we apply the method to predicting PM2.5 concentrations across the continental United States.

Multiple imputation is widely used to handle missing data. Although Rubin's combining rule is simple, it is not clear whether or not the standard multiple imputation inference is consistent when coupled with the commonly-used full sample estimators. This article establishes a unified martingale representation of multiple imputation for a wide class of asymptotically linear full sample estimators. This representation invokes the wild bootstrap inference to provide consistent variance estimation under the correct specification of the imputation models. As a motivating application, we illustrate the proposed method to estimate the average causal effect (ACE) with partially observed confounders in causal inference. Our framework applies to asymptotically linear ACE estimators, including the regression imputation, weighting, and matching estimators. We extend to the scenarios when both outcome and confounders are subject to missingness and when the data are missing not at random.

This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general test statistic and derive its central limit theorem by random matrix theory without a Gaussian population constraint. We then apply the result to estimate the noise variance and test the equality of the smallest roots in generalized spiked models. Simulation studies showed that the proposed test method was correctly sized, and the power outcomes showed the robustness of our statistic to deviations from a Gaussian population. Moreover, our estimator of the noise variance resulted in much smaller mean absolute errors and mean squared errors than existing methods. In contrast to previously developed methods, we eliminated the strict conditions of diagonal or block-wise diagonal form of the population covariance matrix and extend the work to a wider range without the assumption of normality. Thus, the proposed method is more suitable for real problems., 23 pages,3 figures