Conditional maximum likelihood timing recovery

This paper presents a unified framework for the formulation of synchronization algorithms dealing with the general class of Filter-Bank Multi-Carrier (FBMC) communication signals. This is a wide family of signaling formats that includes Orthogonal Frequency Division Multiplexing (OFDM), for instance, as just one of many particular cases. One of the main contributions of this work is the proposal of a novel matrix signal model for so-called flexible FBMC signals, in which no restrictions are imposed on the signal design parameters (i.e., pulse shaping, symbol rate, carrier spacing, sampling frequency, etc.), unlike the type of multicarrier signals currently deployed. As an example of application of the proposed matrix signal model, blind joint time-delay and frequency estimators will be derived under both the Conditional Maximum Likelihood (CML) and the low-SNR Unconditional Maximum Likelihood (UML) principles, for any FBMC signal propagating through an arbitrary multipath channel. These estimators will be specialized first for the case of critically sampled cyclic-prefix OFDM (CP-OFDM) signals in frequency flat fading, leading to simple architectures amenable to a hardware implementation. Later on, and for the low-SNR UML principle, the special case of critically sampled CP-OFDM in multipath channels will be addressed, where a novel synchronizer will be proposed.

We consider the problem of timing recovery for bandlimited, baud-rate sampled systems with intersymbol interference and a timing offset that can be modeled as a combination of a frequency offset and a random walk. We first derive the Cramer–Rao bound (CRB), which is a lower bound on the estimation-error variance for any timing estimator. Conventional timing recovery is based on a phase-locked loop (PLL). We compare the conventional timing recovery method with the CRB for realistic timing parameters for the magnetic recording channel, and observe a 7 dB signal-to-noise ratio gap between the two. Next, we propose a PLL postprocessor based on the maximum a posteriori estimation principle that performs to within 1.5 dB of the CRB. This postprocessor performs time-invariant filtering and time-varying scaling of the PLL timing estimates. The refined timing estimates from the postprocessor are then used to get refined samples by interpolating the samples taken at the PLL's timing estimates. Finally, we present suboptimal implementations that allow a performance-complexity tradeoff.

Attack to security of watermarking is to estimate secret keys used in watermarking communications. The security level of watermarking algorithms can be evaluated by Cramer-Rao Bound (CRB) for the estimation of secret keys. As a widely used method, Add-Spread-Spectrum (Add-SS) watermarking has drawn a lot of attention. Previous work on watermarking security is mainly based on the assumption that the host is Gaussian distributed and ignores the impact of the non-Gaussian characteristics of natural images. With the incorporation of Gaussian Scale Mixture (GSM) model for host signals, this paper presents a theoretical analysis on the security of the Add-SS watermarking algorithms. By giving the CRB and Modified Cramer-Rao Bound (MCRB) for the estimation of secret carriers under Known Message Attack (KMA) and Watermarked Only Attack (WOA), this paper also reveals the factors that may influence the security of Add-SS based watermarking algorithms. Results presented in this paper are very helpful for designing the new generation of secure and robust watermarking system.

In this paper we derive the Modified Cramér-Rao Bound (MCRB) for symbol timing, phase and frequency offset in presence of non-linear self-phase modulation (SPM) in a dispersion compensated long-haul coherent fiber link. We consider dual polarization multilevel quadrature amplitude modulation and multiple span of fiber each associated with optical amplifier. In presence of a realistic low pass filter (LPF) at the receiver front end, we find that SPM degrades the MCRB significantly. Moreover, SPM induces underdamped oscillation on the bounds. Simulation is carried out with self-generated asymmetric pulse to verify the theoretical results.

In analysing panel data in which the dependent variable is a binary choice variable taking values 1 or 0 for success or failure respectively, it is feasible to consider the conditional probabilities of the dependent variable. Under strict exogeneity, this conditional probability equals the expected value of the dependent variable. This treatment calls for a nonlinear function which will ensure that the conditional probability lies between 0 and 1, and such functions yield the probit model and the logit model. This paper discusses an estimation of nonlinear logit panel data model with fixed effects. There are two main estimators for such models: 'unconditional maximum likelihood' and 'conditional maximum likelihood'. Application study was designed to determine the most important factors affecting delayed completion of adjuvant chemotherapy among patients with breast cancer and adjuvant chemotherapy improvement outcomes of patients with breast cancer to determine the relationship between time to chemotherapy and outcome according to breast cancer. The optimal timing from beginning to the end of chemotherapy is known (three months). We hypothesized that prolonged time to chemotherapy would be associated with adverse outcomes. Delayed time to chemotherapy was defined as more three months from the first dose and the last dose of chemotherapy. The study results show that the conditional fixed effects logit estimator is efficient and better than the unconditional pooling and unconditional fixed effects logit estimators. And we find that the most important factors affecting delayed completion of adjuvant chemotherapy among patients are haemoglobin, platelets, and alanine transaminase.

An order-preserving property of the maximum likelihood estimates for the Rasch model

In this paper we compare three frameworks for discriminative training of continuous-density hidden Markov models (CD-HMMs). Specifically, we compare two popular frameworks, based on conditional maximum likelihood (CML) and minimum classification error (MCE), to a new framework based on margin maximization. Unlike CML and MCE, our formulation of large margin training explicitly penalizes incorrect decodings by an amount proportional to the number of mislabeled hidden states. It also leads to a convex optimization over the parameter space of CD-HMMs, thus avoiding the problem of spurious local minima. We used discriminatively trained CD-HMMs from all three frameworks to build phonetic recognizers on the TIMIT speech corpus. The different recognizers employed exactly the same acoustic front end and hidden state space, thus enabling us to isolate the effect of different cost functions, parameterizations, and numerical optimizations. Experimentally, we find that our framework for large margin training yields significantly lower error rates than both CML and MCE training.

The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with ε adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.

It has been known for several years that conditional and mixture maximum likelihood estimates do agree for the dichotomous Rasch model (RM). This equivalence may be attained by a sufficient number of mixing components in a specifically restricted latent-class model. Because the principle of such a semiparametric approach is a general one (Kiefer & Wolfowitz, 1956), it also applies to some other models of the Rasch type having simple sufficient statistics. Exact equivalence regarding the parameter estimates can be shown, for example, for the linear logistic test model, a RM with linearly constrained item parameters, and for the polytomous RM; only almost equivalence is found for the mixed RM. As formal proofs of these results are difficult, the presentation focuses on numerical examples demonstrating the said (almost) equivalence.

The expected cell count for a 2 x 2 contingency table, governed by the noncentral (extended) hypergeometric distribution, is expressed as a terminating continued fraction. The coefficients in the continued fraction are better behaved than the multinomial coefficients required for the usual moment calculation. The expected cell count must be calculated repeatedly in a conditional maximum likelihood analysis of K2 x 2 contingency tables. Since the continued fraction can be easily evaluated, a rapid and numerically stable computational algorithm results. Once this first moment is known, higher moments can be obtained as shown by Harkness (1965, Annals of Mathematical Statistics 36, 938-945). A BASIC program to implement the continued fraction algorithm is given in an appendix.

Link functions are commonly used in count regression analysis, and asymmetric link functions serve as a useful tool for studying imbalanced data. Recently, the field of binary regression has witnessed the emergence of skew probit (sp), skew logit (scobit), logistic arctan (lat), arc transformation of scobit (sat) and soft clipping (sc) besides logit (logistic unit) and probit (probability unit) link functions. However, they have not been well studied in time series analysis. The binary INGARCH model is a popular tool for analyzing binary time series, therefore, these link functions are introduced to this type of model. The parameters of the proposed models are estimated using the conditional maximum likelihood method. The bias reduction of the conditional maximum likelihood estimator is also discussed. A portmanteau test for goodness-of-fit is also given. A simulation is conducted to evaluate the performance of the estimator. All proposed models are empirically validated and compared using real-world data sets, and the related results demonstrate the superiority of the new link functions and the new estimation method.

Conditional likelihood inference in a heteroscedastic functional measurement error model

A novel method for image thresholding using interval type-2 fuzzy set and Bat algorithm

Like other multicarrier schemes, the most likely 5G schemes, Filter Bank Multicarrier (FBMC) and Generalized Frequency Division Multiplexing (GFDM) suffer from carrier frequency offset (CFO) which causes significant degradation in the BER of either modulation scheme. After presenting a brief block level implementation architecture and representation of both FBMC and GFDM, we propose novel usage of Data-Aided (DA) efficient algorithm based on modified Maximum Likelihood (ML) principle for the estimation of CFO in FBMC and GFDM schemes. The estimation performance is analyzed in terms of Mean Square Error (MSE), both in the presence of Gaussian noise and stanford university interim (SUI) channel models. To verify the effectiveness of the proposed estimation, the performance is compared with Cramer-Rao Lower Bound (CRLB) and it is shown that MSE achieves CRLB for moderate and higher values of SNR. we also compare the performance of the proposed estimator with data-aided near maximum likelihood estimator for FBMC under 6-tap Rician channel and Kalman filter based iterative algorithm for GFDM in Gaussian noise.

It is argued that the choice between one-sided and two-sided confidence intervals must be made according to a rule prior to and independent of the data and it is shown that such a rule was found in principle by a statistician about half a century ago. The novel problem with unphysical estimates of a parameter in presence of background is solved in the realm of classical statistics by applying this rule and the principle of maximum likelihood. Optimal confidence intervals are given for the measurement of a bounded magnitude with normal errors, most effective in discriminating a signal next to the bound, and it is shown how to get them in any single case for a bounded discrete variable with background, in general and specifically for Poisson and binomial variables, with two examples of application. The upper limit provided by this method, when the data are consistent with no signal, does not decrease with unphysical estimates going far off the physical values, so removing the last claimed support of Bayesian inference in physics. Procedures are given extending the method to several parameters.