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To compare the performance of a targeted maximum likelihood estimator (TMLE) and a collaborative TMLE (CTMLE) to other estimators in a drug safety analysis, including a regression-based estimator, propensity score (PS)–based estimators, and an alternate doubly robust (DR) estimator in a real example and simulations. The real data set is a subset of observational data from Kaiser Permanente Northern California formatted for use in active drug safety surveillance. Both the real and simulated data sets include potential confounders, a treatment variable indicating use of one of two antidiabetic treatments and an outcome variable indicating occurrence of an acute myocardial infarction (AMI). In the real data example, there is no difference in AMI rates between treatments. In simulations, the double robustness property is demonstrated: DR estimators are consistent if either the initial outcome regression or PS estimator is consistent, whereas other estimators are inconsistent if the initial estimator is not consistent. In simulations with near-positivity violations, CTMLE performs well relative to other estimators by adaptively estimating the PS. Each of the DR estimators was consistent, and TMLE and CTMLE had the smallest mean squared error in simulations.

Making inferences from IRT-based test scores requires accurate and reliable methods of person parameter estimation. Given an already calibrated set of item parameters, the latent trait could be estimated either via maximum likelihood estimation (MLE) or using Bayesian methods such as maximum a posteriori (MAP) estimation or expected a posteriori (EAP) estimation. In addition, Warm’s (Psychometrika 54:427–450, 1989 ) weighted likelihood estimation method was proposed to reduce the bias of the latent trait estimate in unidimensional models. In this paper, we extend the weighted MLE method to multidimensional models. This new method, denoted as multivariate weighted MLE (MWLE), is proposed to reduce the bias of the MLE even for short tests. MWLE is compared to alternative estimators (i.e., MLE, MAP and EAP) and shown, both analytically and through simulations studies, to be more accurate in terms of bias than MLE while maintaining a similar variance. In contrast, Bayesian estimators (i.e., MAP and EAP) result in biased estimates with smaller variability.

When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.

Heston model is the most famous stochastic volatility model in finance. This paper considers the parameter estimation problem of Heston model with both known and unknown volatilities. First, parameters in equity process and volatility process of Heston model are estimated separately since there is no explicit solution for the likelihood function with all parameters. Second, the normal maximum likelihood estimation (NMLE) algorithm is proposed based on the Itô transformation of Heston model. The algorithm can reduce the estimate error compared with existing pseudo maximum likelihood estimation. Third, the NMLE algorithm and consistent extended Kalman filter (CEKF) algorithm are combined in the case of unknown volatilities. As an advantage, CEKF algorithm can apply an upper bound of the error covariance matrix to ensure the volatilities estimation errors to be well evaluated. Numerical simulations illustrate that the proposed NMLE algorithm works more efficiently than the existing pseudo MLE algorithm with known and unknown volatilities. Therefore, the upper bound of the error covariance is illustrated. Additionally, the proposed estimation method is applied to American stock market index S&P 500, and the result shows the utility and effectiveness of the NMLE-CEKF algorithm.

The analysis of the joint cumulative distribution function (CDF) with bivariate event time data is a challenging problem both theoretically and numerically. This paper develops a tensor spline-based sieve maximum likelihood estimation method to estimate the joint CDF with bivariate current status data. The I-splines are used to approximate the joint CDF in order to simplify the numerical computation of a constrained maximum likelihood estimation problem. The generalized gradient projection algorithm is used to compute the constrained optimization problem. Based on the properties of B-spline basis functions it is shown that the proposed tensor spline-based nonparametric sieve maximum likelihood estimator is consistent with a rate of convergence potentially better than n¹ / ³ under some mild regularity conditions. The simulation studies with moderate sample sizes are carried out to demonstrate that the finite sample performance of the proposed estimator is generally satisfactory.

In conditionally heteroscedastic models, the optimal prediction of powers, or logarithms, of the absolute value has a simple expression in terms of the volatility and an expectation involving the independent process. A natural procedure for estimating this prediction is to estimate the volatility in the first step, for instance by Gaussian quasi-maximum-likelihood or by least absolute deviations, and to use empirical means based on rescaled innovations to estimate the expectation in the second step. The paper proposes an alternative one-step procedure, based on an appropriate non-Gaussian quasi-maximum-likelihood estimator, and establishes the asymptotic properties of the two approaches. Asymptotic comparisons and numerical experiments show that the differences in accuracy can be important, depending on the prediction problem and the innovations distribution. An application to indices of major stock exchanges is given.

We present a novel methodology for estimating the parameters of a finite mixture model (FMM) based on partially rank-ordered set (PROS) sampling and use it in a fishery application. A PROS sampling design first selects a simple random sample of fish and creates partially rank-ordered judgement subsets by dividing units into subsets of prespecified sizes. The final measurements are then obtained from these partially ordered judgement subsets. The traditional expectation–maximization algorithm is not directly applicable for these observations. We propose a suitable expectation–maximization algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. We show that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small samples. The results are used to classify a fish population using the length-frequency data.

Amino acid replacement matrices are an essential basis of protein phylogenetics. They are used to compute substitution probabilities along phylogeny branches and thus the likelihood of the data. They are also essential in protein alignment. A number of replacement matrices and methods to estimate these matrices from protein alignments have been proposed since the seminal work of Dayhoff et al. (1972). An important advance was achieved by Whelan and Goldman (2001) and their WAG matrix, thanks to an efficient maximum likelihood estimation approach that accounts for the phylogenies of sequences within each training alignment. We further refine this method by incorporating the variability of evolutionary rates across sites in the matrix estimation and using a much larger and diverse database than BRKALN, which was used to estimate WAG. To estimate our new matrix (called LG after the authors), we use an adaptation of the XRATE software and 3,912 alignments from Pfam, comprising ~50,000 sequences and ~6.5 million residues overall. To evaluate the LG performance, we use an independent sample consisting of 59 alignments from TreeBase and randomly divide Pfam alignments into 3,412 training and 500 test alignments. The comparison with WAG and JTT shows a clear likelihood improvement. With TreeBase, we find that 1) the average Akaike information criterion gain per site is 0.25 and 0.42, when compared with WAG and JTT, respectively; 2) LG is significantly better than WAG for 38 alignments (among 59), and significantly worse with 2 alignments only; and 3) tree topologies inferred with LG, WAG, and JTT frequently differ, indicating that using LG impacts not only the likelihood value but also the output tree. Results with the test alignments from Pfam are analogous. LG and a PHYML implementation can be downloaded from http://atgc.lirmm.fr/LG. [PUBLICATION ABSTRACT]

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

This paper introduces the four parameter transmuted generalized Gompertz distribution which includes the transmuted Gompertz, transmuted generalized exponential, transmuted exponential, Gompertz, generalized exponential and exponential distributions as special cases and studies its statistical properties. Explicit expressions are derived for the quantile, moments, moment generating function and entropies. Maximum likelihood estimation is used to estimate the model parameters. Finally, two applications of the new distribution is illustrated using reliability data sets.