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Epidemiologic screening programs often make use of tests with small, but nonzero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect test with known sensitivity and specificity to a sample of individuals from the population. In this setting, we propose an enhanced inferential approach for use in conjunction with sampling-based bias-corrected prevalence estimation. While ignoring the finite nature of the population can yield markedly conservative estimates, direct application of a standard finite population correction (FPC) conversely leads to underestimation of variance. We uncover a way to leverage the typical FPC indirectly toward valid statistical inference. In particular, we derive a readily estimable extra variance component induced by misclassification in this specific but arguably common diagnostic testing scenario. Our approach yields a standard error estimate that properly captures the sampling variability of the usual bias-corrected maximum likelihood estimator of disease prevalence. Finally, we develop an adapted Bayesian credible interval for the true prevalence that offers improved frequentist properties (i.e., coverage and width) relative to a Wald-type confidence interval. We report the simulation results to demonstrate the enhanced performance of the proposed inferential methods. [ABSTRACT FROM AUTHOR]

This research article introduces a new family of distributions developed using the innovative beta-generated transformation technique. Among these distributions, the focus is on the inverse exponential power distribution, which exhibits unique reverse-J, inverted bathtub, or monotonically increasing hazard functions. This paper thoroughly investigates the distribution's key characteristics and utilizes the maximum likelihood estimation method to determine its associated parameters. To assess the accuracy of the estimation procedure, the researchers conducted a simulation experiment, revealing diminishing biases and mean square errors with increasing sample sizes, even when working with small samples. Moreover, the practical applicability of the proposed distribution is demonstrated by analyzing real-world COVID-19 and medical datasets. The article establishes that the proposed model outperforms existing models by using model selection criteria and conducting goodness-of-fit test statistics. The potential applications of this research extend to various fields where modeling and analyzing hazard functions or survival data are crucial. Additionally, the study contributes to advancing probability theory and statistical inferences. [ABSTRACT FROM AUTHOR]

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimates is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods. [ABSTRACT FROM AUTHOR]

In this research article, we propose and study a new model the so-called Marshal-Olkin Kumaraswamy moment exponential distribution. The new distribution contains the moment exponential distribution, exponentiated moment exponential distribution, Marshal Olkin moment exponential distribution and generalized exponentiated moment exponential distribution as special sub-models. Some significant properties are acquired such as expansion for the density function and explicit expressions for the moments, generating function, Bonferroni and Lorenz curves. The probabilistic definition of entropy as a measure of uncertainty called Shannon entropy is computed. Some of the numerical values of entropy for different parameters are given. The method of maximum likelihood is adopted for estimating the model parameters. We study the behavior of the maximum likelihood estimates for the model parameters using simulation study. A numerical study is performed to evaluate the behavior of the estimates with respect to their absolute biases, standard errors and mean square errors for different sample sizes and for different parameter values. Further, we conclude that the maximum likelihood estimates of the Marshal-Olkin Kumaraswamy moment exponential distribution perform well as the sample size increases. We take advantage of applied studies and offer two applications to real data sets that prove empirically the power of adjustment of the new model when compared to other lifetime distributions. [ABSTRACT FROM AUTHOR]

In Gaussian measurement models, the measurements are given by a known function of the unknown parameter vector, contaminated by additive zero-mean Gaussian noise. When the function is linear, the resulting maximum likelihood estimate (MLE) is well-known to be efficient [unbiased, with a mean square estimation error (MSE) matrix attaining the Cramér–Rao lower bound (CRLB)]. However, when the function is nonlinear, the MLE is only asymptotically efficient. The classical derivation of its asymptotic efficiency uses a first-order perturbation analysis, relying on a “small-errors” assumption, which under subasymptotic conditions turns inaccurate, rendering the MLE generally biased and inefficient. Although a more accurate (higher-order) performance analysis for such cases is of considerable interest, the associated derivations are rather involved, requiring cumbersome notations and indexing. Building on the recent assimilation of tensor computations into signal processing literature, we exploit the tensor formulation of higher-order derivatives to derive a tractable formulation of a higher (up to third-) order perturbation analysis, predicting the bias and MSE matrix of the MLE of parameter vectors in general nonlinear models under subasymptotic conditions. We provide explicit expressions depending on the first three derivatives of the nonlinear measurement function, and demonstrate the resulting ability to predict the “efficiency gap” (relative excess MSE beyond the CRLB) in simulation experiments. We also provide MATLAB code for easy computation of our resulting expressions. [ABSTRACT FROM AUTHOR]

We consider deterministic parameter estimation and the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters. Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models. [ABSTRACT FROM PUBLISHER]

Knowing the time of changes, called change-point (CP), in a process is crucial for engineers to recognize the root cause fast and accurately. Since special causes may induce simultaneous changes in mean and variance, detecting changes in both at once is required. Many methodologies in quality control were developed for detecting changes in either mean or variance only, and process parameters were assumed known often. However, they are rarely known exactly and a small estimation error may lead to unfavorable CP estimates. Fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality. A new mechanism, called fuzzy classification maximum likelihood change-point (FCML-CP) algorithm, is proposed to detect shifts in mean and variance simultaneously. A CP framework is transferred into a mixture model and then a FCML-CP algorithm is created through fuzzy classification maximum likelihood procedures. The proposed FCML-CP can be applied to phase I and II processes without knowledge of in-control process parameters; it can estimate multiple CPs of process mean or/and variance simultaneously. The effectiveness and superiority of FCML-CP are shown by extensive experiments with numerical and real data sets. Specifically, the proposed FCML-CP is superior to the commonly used statistical mixture likelihood approach using expectation–maximization (EM) algorithm; it is much more time-saving especially. The remarkable performance of FCML-CP in detecting CPs for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out-of-control signal resulted from small changes is usually delayed long. [ABSTRACT FROM AUTHOR]

In wireless communication, the multiple-input multiple-output (MIMO) system is a well-known approach to improve the reliability as well as the data rate. In MIMO systems, channel state information (CSI) is typically required at the receiver to detect transmitted signals; however, in practical systems, the CSI is imperfect and contains errors, which affect the overall system performance. In this paper, we propose a novel maximum likelihood (ML) scheme for MIMO systems that is robust to the CSI errors. We apply an optimization method to estimate an instantaneous covariance matrix of the CSI errors in order to improve the detection performance. Furthermore, we propose the employment of the list sphere decoding (LSD) scheme to reduce the computational complexity, which is capable of efficiently finding a reduced set of the candidate symbol vectors for the computation of the covariance matrix of the CSI errors. An iterative detection scheme is also proposed to further improve the detection performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel technique for Instantaneous Frequency (IF) estimation of multi component non stationary signals using Fourier Bessel Series and Time- Varying Auto Regressive (FB-TVAR) model. In the proposed technique, the Fourier-Bessel (FB) expansion decomposes the multi-component non stationary signal into a number of monocomponent signals and TVAR model is used to model each mono-component signal. In TVAR modeling approach the time varying parameters are expanded as a linear combination of basis functions. In this paper, the TVAR parameters are expanded by a discrete cosine basis functions. The maximum likelihood estimation algorithm for model order selection in TVAR models is also discussed. The Instantaneous Frequency (IF) is extracted from the time-varying parameters by calculating the angles of the estimation error filter polynomial roots. The estimation of the TVAR parameters of a multicomponent signal requires the inversion of a large covariance matrix, while the projected technique (FB-TVAR) requires the inversion of a number of comparatively small covariance matrices with better numerical stability properties. Simulation results are presented for Multi component discrete Amplitude and Frequency modulated (AM-FM) signal. [ABSTRACT FROM AUTHOR]

An effective approach termed Recursive Gaussian Maximum Likelihood Estimation (RGMLE) is developed in this paper to suppress 2-D impulse noise. And two algorithms termed RGMLE-C and RGMLE-CS are derived by using spatially-adaptive variances, which are respectively estimated based on certainty and joint certainty & similarity information. To give reliable implementation of RGMLE-C and RGMLE-CS algorithms, a novel recursion stopping strategy is proposed by evaluating the estimation error of uncorrupted pixels. Numerical experiments on different noise densities show that the proposed two algorithms can lead to significantly better results than some typical median type filters. Efficient implementation is also realized via GPU (Graphic Processing Unit)-based parallelization techniques. [ABSTRACT FROM AUTHOR]

The full-information maximum likelihood (FIML) method makes it possible to estimate and analyze structural equation models (SEM) even when data are partially missing, enabling incomplete data to contribute to model estimation. The cornerstone of FIML is the missing-at-random (MAR) assumption. In (unidimensional) computerized adaptive testing (CAT), unselected items (i.e., responses that are not observed) remain at random even though selected items (i.e., responses that are observed) have been associated with a test taker's latent trait that is being measured. In multidimensional adaptive testing (MAT), however, the missingness in the response data partially depends on the unobserved data because items are selected based on various types of information including the covariance among latent traits. This eventually may lead to violations of MAR. This study aimed to evaluate the potential impact such a violation of MAR in MAT could have on FIML estimation performance. The results showed an increase in estimation errors in item parameter estimation when the MAT response data were used, and differences in the level of the impact depending on how items loaded on multiple latent traits. [ABSTRACT FROM AUTHOR]

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