Proposed Maximum Likelihood Estimator Research Articles

Deep partially linear cox model for current status data.

Deep learning has continuously attained huge success in diverse fields, while its application to survival data analysis remains limited and deserves further exploration. For the analysis of current status data, a deep partially linear Cox model is proposed to circumvent the curse of dimensionality. Modeling flexibility is attained by using deep neural networks (DNNs) to accommodate nonlinear covariate effects and monotone splines to approximate the baseline cumulative hazard function. We establish the convergence rate of the proposed maximum likelihood estimators. Moreover, we derive that the finite-dimensional estimator for treatment covariate effects is $\sqrt{n}$-consistent, asymptotically normal, and attains semiparametric efficiency. Finally, we demonstrate the performance of our procedures through extensive simulation studies and application to real-world data on news popularity.

Statistical Inference in Circular Structural Model and Fitting Circles to Noisy Data

It is well known that commonly used algorithms for circle fitting perform poorly when sampling distribution of the points is not symmetric with respect to the circle center, for example, when the points are sampled from a circle arc. To overcome this difficulty we introduce and study a parametric circular structural model. In this model the points on the circumference are assumed to be sampled according to the von Mises distribution with unknown concentration and mean direction parameters. We develop maximum likelihood and method of moments estimators of the circle center and radius, and study their statistical properties. In particular, we show that the proposed maximum likelihood estimator is asymptotically normal and efficient. We also develop a test of uniformity for the sampling distribution along the circle. Based on the derived theoretical results we propose a numerically stable circle fitting algorithm, investigate its accuracy in a simulation study, and illustrate its behavior in a real data example. Supplementary materials for this article are available online.

Controlled Parameter Estimation for The AR(1) Model with Stationary Gaussian Noise

This paper deals with the maximum likelihood estimator for the parameter of first-order autoregressive models driven by the stationary Gaussian noises (Colored noise) together with an input. First, we will find the optimal input that maximizes the Fisher information, and then, with the method of the Laplace transform, both the asymptotic properties and the asymptotic design problem of the maximum likelihood estimator will be investigated. The results of the numerical simulation confirm the theoretical analysis and show that the proposed maximum likelihood estimator performs well in finite samples.

Maximum likelihood estimation in the generalized extreme value regression model for binary data

Generalized extreme value regression model is widely used when the dependent variable Y represents a rare event. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome Y and a set of potential predictors X. In this article we develop a maximum likelihood estimation procedure int he generalized extreme value regression model. We establish the asymptotic properties (existence, consistency and asymptotic normality) of the proposed maximum likelihood estimator.

Reliability assessment of repairable systems with series–parallel structure subjected to hierarchical competing risks under minimal repair regime

In this paper, we seek to propose a model that allows us to evaluate the failure times of a single repairable system represented hierarchically, exposed to competing risks and under a minimal repair framework. Our study can be regarded as an extension of the research presented in Louzada et al. (2019), which comprises the representation of complex systems through a hierarchical structure in series and/or in parallel. For this, we deduce the general form of the model, as well as the likelihood function associated with it, to obtain reliable estimates for the parameters that index the model. In addition, we display the mechanism for generating random numbers based on the presented structure, which enables obtaining point and interval estimates (via parametric bootstrap) in a more convenient way for reliability curves at any level of the system hierarchy. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed maximum likelihood estimators and confidence intervals for the model parameters. Finally, we illustrate the applicability of our model and methods with applications that deal with the reliability modeling of a robotic unit still under development, resulting from a project carried out in partnership between Petrobras and other Brazilian research centers.

Signal Model and Parameter Estimation for Colocated Mimo Radar

In this paper, we consider the signal model and parameter estimation for multiple-input multiple-output (MIMO) radar with colocated antennas on stationary platforms. Considering internal clutter motion, a closed form of the covariance matrix of the clutter signal is derived. Based on the proposed closed form and low rank property of the clutter covariance matrix and by using the singular value decomposition, we have proposed a subspace model for the clutter signal. Following the proposed signal model, we have provided maximum likelihood (ML) estimation for its unknown parameters. Finally, the application of the proposed ML estimation in space time adaptive processing (STAP) is investigated in simulation results. Our ML estimation needs no secondary training data and it can be used in scenarios with nonhomogeneous clutter in range.

Amplitude estimation via maximum likelihood on noisy quantum computer

Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assuming the depolarization noise. We then formulate the problem as a two-parameters estimation problem with respect to the target amplitude parameter and the noise parameter. In particular we show that there exist anomalous target values, where the Fisher information matrix becomes degenerate and consequently the estimation error cannot be improved even by increasing the number of amplitude amplifications. The experimental demonstration shows that the proposed maximum likelihood estimator achieves quantum speedup in the number of queries, though the estimation error saturates due to the noise. This saturated value of estimation error is consistent to the theory, which implies the validity of the depolarization noise model and thereby enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.

Estimation of parameters for load-sharing parallel systems under exponential Pareto distribution

This article deals with the estimation of parameters for the load-sharing parallel system when the underlying distribution of component lifetime is exponential Pareto. The appropriate iterative method is used to get the parameter estimators. And the asymptotic distribution of the proposed maximum likelihood estimator is presented. For the model simplified, the maximum likelihood and best asymptotic unbiased estimators of parameters are obtained. Moreover, the confidence intervals for the parameters are constructed using the parameter bootstrap technique. In the end, some appropriate simulation methods and an example are used to substantiate the proposed methods.

Increased sensitivity and signal-to-noise ratio in diffusion-weighted MRI using multi-echo acquisitions

Post-mortem diffusion MRI (dMRI) enables acquisitions of structural imaging data with otherwise unreachable resolutions - at the expense of longer scanning times. These data are typically acquired using highly segmented image acquisition strategies, thereby resulting in an incomplete signal decay before the MRI encoding continues. Especially in dMRI, with low signal intensities and lengthy contrast encoding, such temporal inefficiency translates into reduced image quality and longer scanning times. This study introduces Multi Echo (ME) acquisitions to dMRI on a human MRI system - a time-efficient approach, which increases SNR (Signal-to-Noise Ratio) and reduces noise bias for dMRI images. The benefit of the introduced ME-dMRI method was validated using numerical Monte Carlo simulations and showcased on a post-mortem brain of a wild chimpanzee. The proposed Maximum Likelihood Estimation echo combination results in an optimal SNR without detectable signal bias. The combined strategy comes at a small price in scanning time (here 30% additional) and leads to a substantial SNR increase (here white matter: ~ 1.6x, equivalent to 2.6 averages, grey matter: ~ 1.9x, equivalent to 3.6 averages) and a general reduction of the noise bias.

A non-data-aided SNR estimator based on maximum likelihood method for communication between orbiters

Signal-to-noise ratio (SNR) is an important metric for performance assessment in numerous scenerios. In order to ensure the reliability and effectiveness of the system performance, plenty of situations require the information of SNR estimate. At the same time, Mars exploration has been a hot topic in recent years, which leads to the research attention of scholars extending to deep space. In this paper, a new SNR estimator related to deep space scene is proposed. On the one hand, the time of essential data transmission is limited in Mars exploration system. On the other hand, the relative position and condition between orbiters vary quickly all the time, which makes it difficult to obtain the accurate and significant information for Mars exploration. Therefore, it is obvious that the information of SNR can promote the system to adjust the signal transmission rate automatically. Subsequently, the estimation of SNR becomes a fundamental research in automatic digital communications. In this paper, an SNR estimation method based on non-data-aided (NDA) with maximum likelihood (ML) estimation is proposed to enhance the accuracy and reliability of Mars exploration process. Additionally, the Cramer-Rao lower bound (CRLB) related to the designed ML algorithm is derived. Finally, the Monte Carlo simulation results demonstrate that the proposed ML estimator algorithm obtains a superior performance when compared to the existing SNR estimators.

A Multidimensional TDOA Association Algorithm for Joint Multitarget Localization and Multisensor Synchronization

This article considers the problem of multitarget localization using time difference of arrival (TDOA) measurements at multiple sensors with misaligned clocks in the presence of data association uncertainty. Sensor synchronization and data association are two essential steps in target localization and tracking to align sensor clocks and to associate measurements from different sensors. In practice, sensor synchronization errors can adversely affect data association performance and vice versa. Although these two processes affect each other, they are usually addressed separately. We propose a novel joint multidimensional association algorithm for multisensor synchronization (JMDA4MS), which performs data association and yields sensor clock offset and target position estimates simultaneously using TDOA measurements. Considering the observability of the unknown parameters, the joint multiframe multidimensional association algorithm is developed as a multiframe extension of the JMDA4MS algorithm. A gating method and a multidimensional plus sequential two-dimensional association approach are utilized to improve the efficiency of the proposed algorithms. The Cramer–Rao lower bound for the proposed maximum likelihood estimator is derived as a performance benchmark. Computer simulations are carried out to evaluate the performance of the proposed algorithms on different scenarios.

Maximum Likelihood Joint Angle and Delay Estimation from Multipath and Multicarrier Transmissions with Application to Indoor Localization over IEEE 802.11ac Radio

In this paper, we tackle the problem of joint angle and delays estimation (JADE) of multiple reflections of a known signal impinging on multiple receiving antennae. Based on the importance sampling (IS) concept, we propose a new non-iterative maximum likelihood (ML) estimator that enjoys guaranteed global optimality and enhanced high-resolution capabilities for both single- and multi-carrier models. The new ML approach succeeds in transforming the original multi-dimensional optimization problem into multiple two-dimensional ones thereby resulting in huge computational savings. Moreover, it does not suffer from the off-grid problems that are inherent to most existing JADE techniques. By exploiting the sparsity feature of a carefully designed pseudo-pdf that is intrinsic to the new estimator, we also propose a novel approach that enables the accurate detection of the unknown number of paths over a wide range of practical signal-to-noise ratios (SNRs). Computer simulations show the distinct advantage of the new ML estimator over state-of-the art JADE techniques both in the single- and multi-carrier scenarios. Most remarkably, they suggest that the proposed IS-based ML JADE is statistically efficient as it almost reaches the Camer-Rao lower bound (CRLB) even in the adverse conditions of low SNR levels. Using real-world channel measurements collected from four access points (APs) with IEEE 802.11ac standard’s setup parameters in an indoor environment, we also show that the proposed ML estimator achieves a localization performance below 15 cm accuracy.

A Faster Maximum-Likelihood Modulation Classification in Flat Fading Non-Gaussian Channels

In this letter, we use squared iterative method with parameter checking to accelerate the convergence rate of expectation/conditional maximization (ECM) algorithm when estimating the channel parameters blindly in flat fading non-Gaussian channels, and further, we proposed automatic modulation classification (AMC) in flat fading non-Gaussian channels based on the proposed maximum likelihood estimator. The numerical results show that the proposed method can accelerate the convergence rate of ECM algorithm, and AMC based on the proposed method is faster than that based on ECM, while the accuracy of the former shows nearly no loss compared with that of the latter.

Evaluation of a Maximum Likelihood Estimator for the Identification of Power Systems Oscillation Modes

In this paper, a maximum likelihood (ML) estimator is applied for the estimation of power system oscillation modes. A regularization term is used in order to improve the estimation. An index is proposed to rank the modes and separate spurious from real modes. The ML estimator is compared with Prony method, and its advantages and limitations are discussed. Both methods are applied to synthetic systems and to real Phasor Measurement Unit (PMU) data acquired from the Brazilian Interconnected Power System (BIPS). The results show that the proposed maximum likelihood estimator is useful to complement and validate the results obtained by Prony analysis.

Maximum likelihood estimation for survey data with informative interval censoring

Interval-censored data may arise in questionnaire surveys when, instead of being asked to provide an exact value, respondents are free to answer with any interval without having pre-specified ranges. In this context, the assumption of noninformative censoring is violated, and thus, the standard methods for interval-censored data are not appropriate. This paper explores two schemes for data collection and deals with the problem of estimation of the underlying distribution function, assuming that it belongs to a parametric family. The consistency and asymptotic normality of a proposed maximum likelihood estimator are proven. A bootstrap procedure that can be used for constructing confidence intervals is considered, and its asymptotic validity is shown. A simulation study investigates the performance of the suggested methods.

Generalized Inflated Discrete Models: A Strategy to Work with Multimodal Discrete Distributions

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than one inflated value. To assess the performance of the proposed maximum likelihood estimator, we conducted Monte Carlo experiments under several scenarios for different levels of inflated probabilities under multinomial, ordinal, Poisson, and zero-truncated Poisson outcomes with covariates. We found that ignoring the inflations leads to substantial bias and poor inference of the inflations—not only for the intercept(s) of the inflated categories but other coefficients as well. Specifically, higher values of inflated probabilities are associated with larger biases. By contrast, the generalized inflated discrete models (GIDMs) perform well with unbiased estimates and satisfactory coverages even when the number of parameters that need to be estimated is quite large. We showed that model fit criteria, such as Akaike information criterion, could be used in selecting the appropriate specifications of inflated models. Lastly, the GIDM was implemented using large-scale health survey data as a comparison to conventional modeling approaches such as various Poisson and Ordered Logit models. We showed that the GIDM fits the data better in general. The current work provides a practical approach to analyze multimodal data that exists in many fields, such as heaping in self-reported behavioral outcomes, inflated categories of indifference and neutral in attitude surveys, large amounts of zero, and low occurrences of delinquent behaviors.

Efficient implementation of the ML estimator for high‐resolution angle estimation in an unmanned ground vehicle

Using a maximum-likelihood (ML) estimator for high-resolution angle estimation is well-suited for automotive radars. It is superior to other estimators in cases of small antenna aperture, small samples, and correlated signals. However, the computing power it requires prevents its widespread implementation. In this study, the authors propose a novel implementation method of the ML estimator that achieves appropriate memory requirements and computational costs by defining new variables. The proposed method is appropriate for practical implementation because calculation of the objective function is based only on independent multiply-add operations and can be easily parallelised. Real measured data from their radar of an unmanned ground vehicle system demonstrates the performance of the proposed method. Experimental results show that the proposed ML estimator is more robust than the conventional MUltiple SIgnal Classification method under conditions of low signal-to-noise ratio and a small number of snapshots.

Maximum likelihood estimation method for dual-rate Hammerstein systems

For a dual-rate sampled Hammerstein controlled autoregressive moving average (CARMA) system, this paper uses the polynomial transformation technology to obtain its dual-rate bilinear identification model which is suitable for the available dual-rate sampled-data, uses the maximum likelihood principle to construct a unified parameter vector of all parameters and an information vector formed by the derivative of the noise variable to the unified parameter vector, and directly identifies the parameters of the linear block and the nonlinear block for the dual-rate Hammerstein CARMA system. The unified parameter vector contains the minimum number of the unknown parameters, and the proposed maximum likelihood estimation algorithm has higher computational efficiency than the over-parameterization model based least squares algorithm.

Joint Channel and Frequency Offset Estimation for Oversampled Perfect Reconstruction Filter Bank Transceivers

Recently, DFT-based oversampled perfect reconstruction filter banks (OPRFB), as a special form of filtered multitone, have shown great promises for applications to multicarrier modulation. Still, accurate frequency synchronization and channel equalization are needed for their reliable operation in practical scenarios. In this paper, we first derive a data-aided joint maximum likelihood (ML) estimator of the carrier frequency offset (CFO) and the channel impulse response (CIR) for OPRFB transceiver systems operating over frequency selective fading channels. Then, by exploiting the structural and spectral properties of these systems, we are able to considerably reduce the complexity of the proposed estimator through simplifications of the underlying likelihood function. The Cramer Rao bound on the variance of unbiased CFO and CIR estimators is also derived. The performance of the proposed ML estimator is investigated by means of numerical simulations under realistic conditions with CFO and frequency selective fading channels. The effects of different pilot schemes on the estimation performance for applications over time-invariant and mobile time-varying channels are also examined. The results show that the proposed joint ML estimator exhibits an excellent performance, where it can accurately estimate the unknown CFO and CIR parameters for the various experimental setups under consideration.

Blind carrier frequency offset estimation for interleaved orthogonal frequency division multiple access uplink with multi‐antenna receiver: algorithms and performance analysis

In this study, for interleaved orthogonal frequency division multiple access uplink with multi-antenna receiver, we propose two generalised carrier frequency offset estimators which, respectively, exploit the subspace theory and maximum-likelihood (ML) criterion. We find that, as long as the numbers of multipaths from two of the users are smaller than the number of antennas at the receiver, both the proposed estimators support fully loaded transmissions. We also derive the theoretical performance lower bound for the proposed ML estimator. The numerical results are then provided, which corroborate the proposed studies.