An investigation of the goodness of fit of the maximum likelihood estimation procedure in factor analysis /

Thesis--Illinois.

A note on maximum likelihood estimation of discrete choice models from the 1978 survey of disability and work /

"November 1982."

Chromatic dispersion compensation using full-field maximum-likelihood sequence estimation

We investigate full-field detection-based maximum-likelihood sequence estimation (MLSE) for chromatic dispersion compensation in 10 Gbit/s OOK optical communication systems. Important design criteria are identified to optimize the system performance. It is confirmed that approximately 50% improvement in transmission reach can be achieved compared to conventional direct-detection MLSE at both 4 and 16 states. It is also shown that full-field MLSE is more robust to the noise and the associated noise amplifications in full-field reconstruction, and consequently exhibits better tolerance to nonoptimized system parameters than full-field feedforward equalizer. Experiments over 124 km spans of field-installed single-mode fiber without optical dispersion compensation using full-field MLSE verify the theoretically predicted performance benefits.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Phylogeny of Thylamys (Didelphimorphia, Didelphidae) species, with special reference to Thylamys karimii

The genus Thylamys Gray, 1843 lives in the central and southern portions of South America inhabiting open and shrub-like vegetation, from prairies to dry forest habitats in contrast to the preference of other Didelphidae genera for more mesic environments. Thylamys is a speciose genus including T. elegans (Waterhouse, 1839), T. macrurus (Olfers, 1818), T. pallidior (Thomas, 1902), T. pusillus (Desmarest, 1804), T. venustus (Thomas, 1902), T. sponsorius (Thomas, 1921), T. cinderella (Thomas, 1902), T. tatei (Handley, 1957), T. karimii (Petter, 1968), and T. velutinus (Wagner, 1842) species. Previous phylogenetic analyses in this genus did not include the Brazilian species T. karimii, which is widely distributed in this country. In this study, phylogenetic analyses were performed to establish the relationships among the Brazilian T. karimii and all other previously analyzed species. We used 402-bp fragments of the mitochondrial cytochrome b gene, and the phylogeny estimates were conducted employing maximum parsimony (MP), maximum likelihood (ML), Bayesian (BY), and neighbor-joining (NJ). The topologies of the trees obtained in the different analyses were all similar and pointed out that T. karimii is the sister taxon of a group constituted of taxa from dry and arid environments named the dryland species. The dryland species consists of T. pusillus, T. pallidior, T. tatei, and T. elegans. The results of this work suggest five species groups in Thylamys. In one of them, T. velutinus and T. kariimi could constitute a sister group forming one Thylamys clade that colonized Brazil.

Phylogeny and circumscription of Sapindaceae revisited: molecular sequence data, morphology and biogeography support recognition of a new family, Xanthoceraceae

Background and aims Recent studies have adopted a broad definition of Sapindaceae that includes taxa traditionally placed in Aceraceae and Hippocastanaceae, achieving monophyly but yielding a family difficult to characterize and for which no obvious morphological synapomorphy exists. This expanded circumscription was necessitated by the finding that the monotypic, temperate Asian genus Xanthoceras, historically placed in Sapindaceae tribe Harpullieae, is basal within the group. Here we seek to clarify the relationships of Xanthoceras based on phylogenetic analyses using a dataset encompassing nearly 3/4 of sapindaceous genera, comparing the results with information from morphology and biogeography, in particular with respect to the other taxa placed in Harpullieae. We then re-examine the appropriateness of maintaining the current broad, morphologically heterogeneous definition of Sapindaceae and explore the advantages of an alternative family circumscription. Methods Using 243 samples representing 104 of the 142 currently recognized genera of Sapindaceae s. lat. (including all in Harpullieae), sequence data were analyzed for nuclear (ITS) and plastid (matK, rpoB, trnD-trnT, trnK-matK, trnL-trnF and trnS-trnG) markers, adopting the methodology of a recent family-wide study, performing single-gene and total evidence analyses based on maximum likelihood (ML) and maximum parsimony (MP) criteria, and applying heuristic searches developed for large datasets, viz, a new strategy implemented in RAxML (for ML) and the parsimony ratchet (for MP). Bootstrap analyses were performed for each method to test for congruence between markers. Key results Our findings support earlier suggestions that Harpullieae are polyphyletic: Xanthoceras is confirmed as sister to all other sampled taxa of Sapindaceae s. lat.; the remaining members belong to three other clades within Sapindaceae s. lat., two of which correspond respectively to the groups traditionally treated as Aceraceae and Hippocastanaceae, together forming a clade sister to the largely tropical Sapindaceae s. str., which is monophyletic and morphologically coherent provided Xanthoceras is excluded. Conclusion To overcome the difficulties of a broadly circumscribed Sapindaceae, we resurrect the historically recognized temperate families Aceraceae and Hippocastanaceae, and describe a new family, Xanthoceraceae, thus adopting a monophyletic and easily characterized circumscription of Sapindaceae nearly identical to that used for over a century.