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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 paper, we study the statistical inference of the generalized inverted exponential distribution with the same scale parameter and various shape parameters based on joint progressively type-II censored data. The expectation maximization (EM) algorithm is applied to calculate the maximum likelihood estimates (MLEs) of the parameters. We obtain the observed information matrix based on the missing value principle. Interval estimations are computed by the bootstrap method. We provide Bayesian inference for the informative prior and the non-informative prior. The importance sampling technique is performed to derive the Bayesian estimates and credible intervals under the squared error loss function and the linex loss function, respectively. Eventually, we conduct the Monte Carlo simulation and real data analysis. Moreover, we consider the parameters that have order restrictions and provide the maximum likelihood estimates and Bayesian inference. [ABSTRACT FROM AUTHOR]

In high-speed analog-to-digital converters (ADCs), two main factors contribute to high power consumption. The first is the super linear relationship with the sampling rate; i.e., by doubling the sampling rate, the power consumption more than doubles. The second factor arises from the consumption of analog circuitry responsible to mitigate the jitter noise. By employing a multichannel sampling system, one can achieve high sampling rates by incorporating multiple low sampling-rate channels, which results in a linear scaling of power consumption with the number of channels. The main drawback of this system is the timing mismatch between the sampling channels. In this paper, we intend to jointly compensate the jitter noise and the timing mismatch between the channels using statistical methods. We first approximate the acquisition system and derive a stochastic model. Then, we propose an iterative maximum likelihood algorithm to estimate the parameters of the input signal. We further evaluate the Cramér-Rao lower bound (CRLB) for the estimation error to examine the proposed algorithm. Simulation results indicate that our algorithm is capable of closely following the CRLB curve for reasonable values of jitter noise and a wide range of timing mismatch errors. Moreover, it is shown that the mismatch-compensated multichannel sampling system performs almost equivalently to a single-channel high rate sampler without having its shortcomings. [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]

Wide-swath synthetic aperture radar (SAR) missions with short revisit times, such as Sentinel-1 and the planned NISAR and Tandem-L, provide an unprecedented wealth of interferometric SAR (InSAR) time series. However, the processing of the emerging Big Data is challenging for state-of-the-art InSAR analysis techniques. This contribution introduces a novel approach, named Sequential Estimator, for efficient estimation of the interferometric phase from long InSAR time series. The algorithm uses recursive estimation and analysis of the data covariance matrix via division of the data into small batches, followed by the compression of the data batches. From each compressed data batch artificial interferograms are formed, resulting in a strong data reduction. Such interferograms are used to link the “older” data batches with the most recent acquisitions and thus to reconstruct the phase time series. This scheme avoids the necessity of reprocessing the entire data stack at the face of each new acquisition. The proposed estimator introduces negligible degradation compared to the Cramér–Rao lower bound under realistic coherence scenarios. The estimator may therefore be adapted for high-precision near-real-time processing of InSAR and accommodate the conversion of InSAR from an offline to a monitoring geodetic tool. The performance of the Sequential Estimator is compared to state-of-the-art techniques via simulations and application to Sentinel-1 data. [ABSTRACT FROM PUBLISHER]

We study the problem of identifying multiple rumor or infection sources in a network under the susceptible-infected model, and where these sources may start infection spreading at different times. We introduce the notion of an abstract estimator that, given the infection graph, assigns a higher value to each vertex in the graph it considers more likely to be a rumor source. This includes several of the single-source estimators developed in the literature. We introduce the concepts of a quasi-regular tree and a heavy center, which allows us to develop an algorithmic framework that transforms an abstract estimator into a two-source joint estimator, in which the infection graph can be thought of as covered by overlapping infection regions. We show that our algorithm converges to a local optimum of the estimation function if the underlying network is a quasi-regular tree. We further extend our algorithm to more than two sources, and heuristically to general graphs. Simulation results on both synthetic and real-world networks suggest that our algorithmic framework outperforms several existing multiple-source estimators, which typically assume that all sources start infection spreading at the same time. [ABSTRACT FROM PUBLISHER]

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]

This paper deals with area-based subpixel image registration under the rotation-isometric scaling-translation transformation hypothesis. Our approach is based on parametrical modeling of geometrically transformed textural image fragments and maximum-likelihood estimation of the transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments' texture, the proposed estimator \mboxML_\mathrmfBm (ML stands for “maximum likelihood” and fBm stands for “fractal Brownian motion”) has the ability to better adapt to real image texture content compared with other methods relying on universal similarity measures such as mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g., for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlations between registered images show that the \mboxML_\mathrmfBm estimator offers significant improvement compared with other state-of-the-art methods. It reduces translation vector, rotation angle, and scaling factor estimation errors by a factor of about 1.75–2, and it decreases the probability of false match by up to five times. In addition, an accurate confidence interval for \mboxML_\mathrmfBm estimates can be obtained from the Cramér–Rao lower bound on rotation-scaling-translation parameter estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images, and geometrical transformation parameters. [ABSTRACT FROM AUTHOR]