Maximum Likelihood Stacking in White Gaussian Noise with Unknown Variances

Examining the robustness properties of maximum likelihood (ML) estimators of parameters in exponential power and generalized t distributions has been considered together. The well-known asymptotic properties of ML estimators of location, scale and added skewness parameters in these distributions are studied. The ML estimators for location, scale and scale variant (skewness) parameters are represented as an iterative reweighting algorithm (IRA) to compute the estimates of these parameters simultaneously. The artificial data are generated to examine performance of IRA for ML estimators of parameters simultaneously. We make a comparison between these two distributions to test the fitting performance on real data sets. The goodness of fit test and information criteria approve that robustness and fitting performance should be considered together as a key for modeling issue to have the best information from real data sets.

Maximum likelihood (ML) amplitude and noise variance estimation without having to jointly estimate the frequency and the phase and based only on information from the noisy received signal magnitude, is studied for a single sinusoid in complex additive white Gaussian noise. This estimation problem is equivalent to the classic problem of parameter estimation for the Rician distribution. While solving the likelihood equation is impossible in general, we propose a new approach based on a large argument approximation. For the case with known noise variance, a closed-form ML amplitude estimator is obtained, which outperforms the conventional root-mean-square estimator. For the case with unknown noise variance, the closed-form joint amplitude and noise variance estimators obtained do not require prior knowledge of one another.

This chapter reviews the rationale for the use of haplotypes in association-based testing, discusses statistical issues related to haplotype uncertainty that complicate the analysis, then gives practical guidance for testing haplotype-based associations with phenotype or outcome trait, first of candidate gene regions and then for the genome as a whole. Haplotypes are interesting for two reasons: First, they may be in closer LD with a causal variant than any single measured SNP, and therefore may enhance the coverage value of the genotypes over single SNP analysis. Second, haplotypes may themselves be the causal variants of interest and some solid examples of this have appeared in the literature. This chapter discusses three possible approaches to incorporation of SNP haplotype analysis into generalized linear regression models: (1) a simple substitution method involving imputed haplotypes; (2) simultaneous maximum likelihood (ML) estimation of all parameters, including haplotype frequencies and regression parameters; and (3) a simplified approximation to full ML for case-control data. Examples of the various approaches for a haplotype analysis of a candidate gene are provided. We compare the behavior of the approximation-based methods and show that in most instances the simpler methods hold up well in practice. We also describe the practical implementation of genome-wide haplotype risk estimation and discuss several shortcuts that can be used to speed up otherwise potentially very intensive computational requirements.

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

Thermal noise affects polarimetric measurements, but a first order noise correction can be applied, if the noise variance (or power) is known. This paper deals with the estimation of the noise variance and the signal-to-noise ratio (SNR) of the cross-polarized channels in polarimetric synthetic aperture radar (SAR) data. Cramér-Rao Lower Bounds (CRLB) and maximum likelihood (ML) estimators are derived. The ML noise variance estimator is unbiased and efficient, while the ML SNR estimator is biased, but an unbiased SNR estimator can be derived from the biased one. It is also shown that commonly used noise variance and SNR estimators are biased. The results are finally validated using TerraSAR-X fully-polarimetric data.

A maximum likelihood (ML) estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise. This ML estimator can be realized as a pair of receiver prefilters followed by a cross correlator. The time argument at which the correlator achieves a maximum is the delay estimate. The ML estimator is compared with several other proposed processors of similar form. Under certain conditions the ML estimator is shown to be identical to one proposed by Hannan and Thomson [10] and MacDonald and Schultheiss [21]. Qualitatively, the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and, simultaneously, to suppress the noise power. The same type of prefiltering is provided by the generalized Eckart filter, which maximizes the S/N ratio of the correlator output. For low S/N ratio, the ML estimator is shown to be equivalent to Eckart prefiltering.

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.

For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning (FEEL). OAC, however, hinges on accurate channel-gain precoding and strict synchronization among edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for FEEL and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML (SP-ML) estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our SP-ML estimator is linear in the packet length, and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is not severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.

In this paper, we study distributed estimation with wireless sensor networks (WSN) when channel estimation is imperfect. A robust distributed maximum likelihood (ML) estimator of the unknown parameter is proposed, which improves the performance of the traditional ML estimator with imperfect channel estimation. By maximizing the effective signal to noise ratio (SNR) at the fusion center (FC), we find that the optimal length of the training sequence is the square root of the length of the quantized observation at each node. Simulations are provided to evaluate the performance of the robust method and to validate the theoretical optimal length.

The reverberation power spectral density (PSD) is often required for dereverberation and noise reduction algorithms. In this work, we compare two maximum likelihood (ML) estimators of the reverberation PSD in a noisy environment. In the first estimator, the direct path is first blocked. Then, the ML criterion for estimating the reverberation PSD is stated according to the probability density function of the blocking matrix (BM) outputs. In the second estimator, the speech component is not blocked. Instead, the ML criterion for estimating the speech and reverberation PSD is stated according to the probability density function of the microphone signals. To compare the expected mean square error (MSE) between the two ML estimators of the reverberation PSD, the Cramer–Rao Bounds (CRBs) for the two ML estimators are derived. We show that the CRB for the joint reverberation and speech PSD estimator is lower than the CRB for estimating the reverberation PSD from the BM outputs. Experimental results show that the MSE of the two estimators indeed obeys the CRB curves. Experimental results of multimicrophone dereverberation and noise reduction algorithm show the benefits of using the ML estimators in comparison with another baseline estimators.

Estimating the failure rate of the log-logistic distribution by smooth adaptive and bias-correction methods

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.

&lt;div class="section abstract"&gt; &lt;div class="htmlview paragraph"&gt;This recommended practice aims to establish a common output format of crash-related data recorded and stored within certain electronic components currently installed in many light-duty vehicles. This document pertains only to the post-download format of such data and is not intended to standardize the format of the data stored within any on-board storage unit, or to standardize the method of data recording, storing, or extraction.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;Historically, crash data recording technology in light-duty vehicles has developed and evolved based on differing technical needs of manufacturers and their customers without industry standards or government regulation. As a result, wide variations currently exist among vehicle manufacturers regarding the scope and extent of recorded data. This document is intended to be a compilation of data elements that various manufacturers are currently recording, as well as those elements reasonably predicted to be recorded in the foreseeable future, and establishes a common output format of those data elements.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;The scope of this document is deliberately restricted to providing output data formatting guidelines, only. It is not intended to standardize or mandate the recording of any specific data elements or to specify a minimum data set. This restriction in the scope is to avoid imposing constraints on the type of data recorded, the method of gathering and storing data, and the pre-and/or post-processing of data that may be used by various vehicle/device manufacturers as a matter of proprietary design. The committee recognized that, given the lack of societal consensus regarding the acceptability of on-board data recording devices, and has therefore avoided specific recommendations concerning whether event data recorders should be equipped on motor vehicles, and whether, when implemented, a particular type, quantity, and manner of data collection should be used.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;Readers of this series of documents are advised to examine the validity and accuracy of VEDI event data in conjunction with the results from the traditional accident reconstruction practice. Since VEDI event data are acquired only from the on-board electronics systems, they may have not accurately capture the actual dynamics of the vehicle during the accident, or may not contain the full range or length of data during the event.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;This document is one of a multi-volume J1698 series of documents and provides general concepts and common definitions of event data recording. J1698-1 provides definitions of event data and J1698-2 provides data extraction protocols.&lt;/div&gt; &lt;/div&gt;

Cooperative communication combats the effects offadingwithoutthe need for multiple antennas.The cooperative networks use multiple distributed nodes that virtually behave like multiple antennas each having their own local oscillators. But the oscillators cause multiple Carrier Frequency Offsets (CFO), unknown channel gains and Multiple Timing Offsets (MTO). For a good performance of the system perfect synchronization is needed which is achieved by estimation and compensation of multiple offsets. Also, the coverage and capacity can be improved by employing intermediate nodes called relays within cooperative networks. These cooperative relay networks can perform in a better manner even when considering MCFOs, MTOs and unknown channel gains by having more computationally efficient decoders that can use Maximum Likelihood (ML) estimation subject to the Cramer-Rao Lower Bound (CRLB) on the variance of any impartial estimate. The simulation results show that frequency offset still exist after Amplify and Forward (AF) relaying. The performance of a conventional cooperative network seems to have improved with respect to Bit Error Rate of the system when an AF relay is hosted. The estimate of the frequency offset is chosen such that it gives the signal, a high probability of occurrence using ML estimator. In ML estimate, since the bias and variance is difficult to compute, a lower bound called the CRLB on the variance of any unbiased estimate is derived which is satisfied by the ML estimator.Keywords: AF, Cooperative Communication, CFO, ML Estimation and Compensation, OFDM