Improved inference for MCP-Mod approach using time-to-event endpoints with small sample sizes.

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

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 the present paper a mixed approach is proposed for the simultaneously estimation of regression and correlation structure parameters in multivariate probit models using generalized estimating equations for the former and pseudo-score equations for the latter. The finite sample properties of the corresponding estimators are compared to estimators proposed by Qu, Williams, Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994) using generalized estimating equations for both sets of parameters via a Monte Carlo experiment. As a `reference' estimator for an equicorrelation model, the maximum likelihood (ML) estimator of the random effects probit model is calculated. The results show the mixed approach to be the most robust approach in the sense that the number of datasets for which the corresponding estimates converged was largest relative to the other two approaches. Furthermore, the mixed approach led to the most efficient non-ML estimators and to very efficient estimators for regression and correlation structure parameters relative to the ML estimator if individual covariance matrices were used.

In recent years, person reidentification has received growing attention with the increasing popularity of intelligent video surveillance. This is because person reidentification is critical for human tracking with multiple cameras. Recently, keep it simple and straightforward (KISS) metric learning has been regarded as a top level algorithm for person reidentification. The covariance matrices of KISS are estimated by maximum likelihood (ML) estimation. It is known that discriminative learning based on the minimum classification error (MCE) is more reliable than classical ML estimation with the increasing of the number of training samples. When considering a small sample size problem, direct MCE KISS does not work well, because of the estimate error of small eigenvalues. Therefore, we further introduce the smoothing technique to improve the estimates of the small eigenvalues of a covariance matrix. Our new scheme is termed the minimum classification error-KISS (MCE-KISS). We conduct thorough validation experiments on the VIPeR and ETHZ datasets, which demonstrate the robustness and effectiveness of MCE-KISS for person reidentification.

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 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.

Ordinal regression is used to model the ordinal response variable as functions of several explanatory variables. The most commonly used model for ordinal regression is the proportional odds model (POM). The classical technique for estimating the unknown parameters of this model is the maximum likelihood (ML) estimator. However, this method is not suitable for solving problems with extreme observations. A robust regression method is needed to handle the problem of extreme points in the data. This study proposes Huber M-estimator as a robust method to estimate the parameters of the POM with a logistic link function and polytomous explanatory variables. This study assesses ML estimator performance and the robust method proposed through an extensive Monte Carlo simulation study conducted using statistical software, R. Measurement for comparisons are bias, RMSE, and Lipsitzs' goodness of fit test. Various sample sizes, percentages of contamination, and residual standard deviations are considered in the simulation study. Preliminary results show that Huber estimates provide the best results for parameter estimation and overall model fitting. Huber's estimator has reached a 50% breakdown point for data containing extreme points that are quite far from most points. In addition, the presence of extreme points that have only a distance of two times far from most points has no major impact on ML estimates. This means that the estimates for ML and Huber may yield the same results if the model's residual values are between -2 and 2. This situation may also occur for data with a percentage of contamination below 5%.

In estimation theory, the asymptotic (in the number of samples) efficiency of the Maximum Likelihood (ML) estimator is a well known result [1]. Nevertheless, in some scenarios, the number of snapshots may be small. We recently investigated the asymptotic behavior of the Stochastic ML (SML) estimator at high Signal to Noise Ratio (SNR) and finite number of samples [2] in the array processing framework: we proved the non-Gaussiannity of the SML estimator and we obtained the analytical expression of the variance for the single source case. In this paper, we generalize these results to multiple sources, and we obtain variance expressions which demonstrate the non-efficiency of SML estimates.

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

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in studies with modest samples. Bayesian estimation is a logical alternative to ML for LGMs, but there is a lack of research providing guidance on when Bayesian estimation may be preferable to ML or vice versa. This study compared the performance of Bayesian versus ML estimators for LGMs by evaluating their accuracy via Monte Carlo (MC) simulations. For the MC study, longitudinal data sets were generated and estimated using LGM via both ML and Bayesian estimation with three different priors, and parameter recovery across the two estimators was evaluated to determine their relative performance. The findings suggest that ML estimation is a reasonable choice for most LGMs, unless it fails to converge, which can occur with limiting data situations (i.e., just a few time points, no covariate or outcome, modest sample sizes). When models do not converge using ML, we recommend Bayesian estimation with one caveat that the influence of the priors on estimation may have to be carefully examined, per recent recommendations on Bayesian modeling for applied researchers.

Laser pointing systems for small targets are mainly confronted with two pointing errors, jitter and boresight, arising due to atmospheric turbulence, mechanical vibrations and errors in optical alignment. Knowledge of these parameters provides information about the quality of the pointing and tracking system. In the past, several techniques have been investigated to estimate these parameters from returned laser signals. These include the key ratio technique, the chi-squared method and the maximum likelihood (ML) estimation technique. These techniques have been studied in the literature for Gaussian irradiance profiles. In particular, the ML estimation technique has been found to provide excellent results. In this paper, we extend the ML estimation technique from Gaussian profiles to near-Gaussian irradiance profiles. Our results show that the modified estimator performs much better than a direct application of the original ML estimator.

The EM algorithm is a widely used technique for finding maximum likelihood (ML) estimates when the data are not fully observed. Despite its popularity for computing ML estimates in unrestricted problems and the need for simplified computations for problems with equality and inequality restrictions, there have been few applications of the algorithm to restricted ML estimation. The EM algorithm is presented for restricted ML estimation and provides its applications to the probit model under equality and inequality restrictions using two small data sets.

Coherent processing of data from distributed HF receivers requires the receivers to be synchronized to an accuracy within fractions of a wavelength. The HF band extends from 3 MHz to 30 MHz and has wavelengths corresponding to time delays ranging from approximately 33 ns to 333 ns. Thus the receivers must be synchronized to within a few nanoseconds. This is typically beyond the capabilities of even GPS-disciplined oscillators. Traditional clock synchronization methods require distributing a common reference signal to all the receivers, either by cables or by using a local reference transmitter. Both these approaches introduce extra cost and complexity. In this paper, we present an approach for clock synchronization which uses the coherent component of wideband ambient HF background noise to estimate time delays between receivers. The approach exploits the flexibility of inexpensive broadband direct-conversion digital receivers in the 3 - 30 MHz band. Two techniques are presented for measuring time delays between receivers: 1) Time-domain Green's Function estimator based on an approach recently used in underwater acoustics, and 2) an optimal Maximum Likelihood (ML) estimator. Both estimators are shown to choose the maximum of particular generalized cross correlations. The Camer-Rao Lower Bound (CRLB) for time delay estimation from ambient noise is also derived and simulation results are presented that demonstrate the performance of the estimators. For low signal to noise ratio (SNR) or low time-bandwidth product (TBP), the estimators do not achieve the CRLB due to peak ambiguities in the generalized cross correlations. However, for sufficiently large SNR and TBP, we demonstrate that the ML estimator is able to overcome the peak ambiguities and achieve the CRLB. In this case, the ML estimator is able to achieve sub-nanosecond RMS delay errors using a 2.5 s observation of 2 MHz bandwidth isotropic HF ambient noise. Thus the ML estimator is the preferred method for synchronizing the distributed receivers.

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.