Conditional Maximum Likelihood Estimator Research Articles

A novel bounded ℤ-valued autoregressive model with its application on crime data

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Maximum-likelihood estimation of the Po-MDDRCINAR(p) model with analysis of a COVID-19 data

Integer-valued data are frequently encountered in time series studies. A pth-order mixed dependence-driven random coefficient integer-valued autoregressive time series model (Po-MDDRCINAR(p)) in view of binomial and negative binomial operators, where the innovation sequence follows a Poisson distribution, is investigated to provide meaningful theoretical explanations. Strict stationary and ergodicity of the model are demonstrated. Furthermore, the conditional least-squares and conditional maximum-likelihood methods are adopted to estimate the parameters, where the asymptotic characterization of the estimators is derived. Finite-sample properties of the conditional maximum-likelihood estimator are examined in relation to the widely used conditional least-squares estimator. The conclusion is that, if the Poisson assumption of the innovation sequence can be justified, conditional maximum-likelihood method performs better in terms of MADE and MSE. Finally, the practical performance of the model is illustrated by a set of COVID-19 data of suspected cases in China with a comparison with relevant models that exist so far in the literature.

Cox regression model with doubly truncated and interval-censored data

Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.

Clinical and functional outcomes of locked plating vs. cerclage compression wiring for AO type C patellar fractures– a retrospective single-center cohort study

Abstract Purpose Although “tension-band wiring” is still commonly used to stabilize patellar fractures, the technique has recently been scrutinized due to biomechanical insufficiency. Consequently, the AO Foundation renamed the principle to compression cerclage wiring (CCW). Several studies propose favorable outcomes when utilizing locked plating (LP). This study aims to compare outcome of CCW and LP for complex patellar fractures. Methods A retrospective, single-center cohort study was performed on patients who underwent operative treatment for (AO 34 C-Type) patellar fractures between April 2013 and March 2023. Patients with a 12 month follow up were included. We grouped and compared patients based on the applied treatment strategy: group LP vs. group CCW. Primary outcome parameters included implant-related complications and revision surgeries. Secondary outcomes were length of stay, return to work and 12 months functional outcome (Lysholm score). Odd ratios for complications and revisions were calculated using the conditional Maximum Likelihood Estimate. The threshold for statistical significance was set at p < 0.05. Results Of 145 patients, 63 could be included (group LP: n = 23 and group CCW: n = 40). Fractures in group LP were significantly more complex in regard to AO Classification (p < 0.001), number of fragments (p < 0.001) and degree of comminution (p < 0.001), yet odds of complications were significantly lower in group LP (OR: 0.147; 95%CI: 0.015–0.742; p = 0.009). K-wire migration was the most common complication in group CCW (20%). Odds of revision surgery were significantly lower in group LP (OR: 0.000; 95%CI: 0.000-1.120; p = 0.041). The average Lysholm score at one year was favorable in both groups (89.8; SD: 11.9 in group LP and 90.6; SD: 9.3 in group CCW; n.s.). Conclusion In our study cohort, LP was routinely chosen for more complex fracture morphologies; nevertheless the data implies that LP may be considered as the superior fixation technique in regard to complications and revision operations. Especially, K-wire migration occurs frequently after CCW. The one year functional outcome was comparable between the groups, with both demonstrating good results. Prospective randomized studies are indicated to validate our findings.

Estimasi Parameter Model Regresi Logistik Biner dengan Conditional Maximum Likelihood Estimation pada Data Panel

Binary logistic regression models can be used on panel data with categorical responses that experience repeated measurements based on time. This study aims to determine the factors that influence the Human Development Index in South Sulawesi Province in 2015-2019. Data were analyzed through binary logistic regression with fixed effect model approach through Conditional Maximum Likelihood Estimation (CMLE) for panel data. The results of this study indicate that the variables that have a significant effect are life expectancy (X1), school length expectancy (X2) and the average length of schooling (X3). Obtained the probability value of districts/cities that have a medium low and medium high human development index with a classification accuracy of 56.25%.

A mixed BAR(1) model driven by serially dependent innovation with application

To better analyze dependent count data with bounded support, this paper proposes a first-order mixture binomial autoregressive (BAR(1)) model, which is constructed via making use of the Pegram operator, where the innovation processes are assumed to be serially dependent to the observation rather than independent. The new model not only inherits the advantages of existing mixture BAR(1) models while also overcoming their shortcomings, but also does well in explaining binomial overdispersion and zero inflation. We infer various statistical properties of the process, including conditional moments, moments and autocovariance functions. The EM algorithm is employed to calculate the conditional maximum likelihood estimate. To evaluate the performance of obtained estimates, some simulation studies are conducted. Furthermore, the forecasting problem for the proposed model is also discussed. To show the applicability of our model, an application to proposition data set is conducted and we compare our model to some competitive integer-valued time series models with bounded support.

On the sieve M-estimation for a special bilinear time series model with time-functional variance noises

. The bilinear model has been frequently used in fields like control theory and economics to model seismic data. In this article, time-functional variance (TFV) noises are embedded into a specific bilinear model. We propose a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator (GMLE) with a sieve method and then provide various inferential techniques based on this GMLE. It is shown that under the finite fourth moment of errors, the GMLE is consistent and asymptotically normally distributed. A simulation study and analysis of real data are additionally carried out to evaluate GMLE’s finite sample performance.

MCMC conditional maximum likelihood for the two-way fixed-effects logit

. We propose a Markov Chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for the two-way fixed-effects logit model for dyadic data, typically used in network analyses. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in- and out-degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of an extensive simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to logit models for binary panel data with both subject and time-fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small, concentrated, and sparse networks or with rare events in panel data.

Conditional maximum-likelihood estimation in probability-based multistage designs

Conditional maximum-likelihood estimation in probability-based multistage designs

Estimating the size of a closed population by modeling latent and observed heterogeneity.

The paper extends the empirical likelihood (EL) approach of Liu etal. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

Higher-Order INAR Model Based on a Flexible Innovation and Application to COVID-19 and Gold Particles Data

INAR models have the great advantage of being able to capture the conditional distribution of a count time series based on their past observations, thus allowing it to be tailored to meet the unique characteristics of count data. This paper reviews the two-parameter Poisson extended exponential (PEE) distribution and its corresponding INAR(1) process. Then the INAR of order p (INAR(p)) model that incorporates PEE innovations is proposed, its statistical properties are presented, and its parameters are estimated using conditional least squares and conditional maximum likelihood estimation methods. Two practical data sets are analyzed and compared with competing INAR models in an effort to gauge the performance of the proposed model. It is found that the proposed model performs better than the competitors.

A new First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset

Option Pricing and Portfolio Optimization under a Multi-Asset Jump-Diffusion Model with Systemic Risk

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index (e.g., S&P500), along with several low-activity securities infrequently traded on financial markets. The model retains tractability even as the number of securities increases. The proposed framework allows for constructing models with common and asset-specific jumps with normally or exponentially distributed sizes. One of the main features of the model is the possibility of estimating parameters for each asset price process individually. We present the conditional maximum likelihood estimation (MLE) method for fitting asset price processes to empirical data. For the case with common jumps only, we derive a closed-form solution to the conditional MLE method for ordinary assets that works even if the data are incomplete and asynchronous. Alternatively, to find risk-neutral parameters, the least-square method calibrates the model to option values. The number of parameters grows linearly in the number of assets compared to the quadratic growth through the correlation matrix, which is typical for many other multi-asset models. We delve into the properties of the proposed model, its parameter estimation using the MLE method and least-squares technique, the evaluation of VaR and CVaR metrics, the identification of optimal portfolios, and the pricing of European-style basket options. We propose a Laplace-transform-based approach to computing Value at Risk (VaR) and conditional VaR (also known as the expected shortfall) of portfolio returns. Additionally, European-style basket options written on the extreme and average stock prices or returns can be evaluated semi-analytically. For numerical demonstration, we examine a combination of the SPDR S&P 500 ETF (as a systemic risk asset) with eight ordinary assets representing diverse industries. Using historical assets and options prices, we estimate the real-world and risk-neutral parameters of the model with common jumps, construct several optimal portfolios, and evaluate various basket options with the eight assets. The results affirm the robustness and efficiency of the estimation and evaluation methodologies. Computational results are compared with Monte Carlo estimates.

Wind speed prediction using non-gaussian model based on Kumaraswamy distribution

ABSTRACT Wind power is a clean source of energy that not only helps in meeting the growing electricity demand but can also play a profound role in transforming the global energy distribution to mitigate the impact of climate change. Accurate forecasting of wind speed is a crucial factor of power system management. The present endeavor focuses on the development of a non-gaussian framework, Kumaraswamy seasonal autoregressive moving average (KSARMA), to model and forecast the wind speed data of 12 locations across the Indian subcontinent. The monthly wind speed dataset during the period 2003 to 2019 has been utilized to perform the analysis. Diagnostic analysis, Akaike’s information criterion (AIC), and conditional maximum likelihood estimator have been used to select the best-fit model for each location. The correlation coefficient between observed and predicted values for all the locations ranges from 0.77 to 0.93. The root mean squared error (RMSE) was found to lie in 0.04 to 0.16 whereas the mean absolute percentage error (MAPE) was observed in 0.06 to 0.2. A comparison of the proposed KSARMA model with the recently developed beta seasonal autoregressive moving average (βSARMA) and Kumaraswamy autoregressive moving average (KARMA) models has also been facilitated. Error estimates such as root mean squared error (RMSE) and mean absolute percentage error (MAPE) reveal that the KSARMA model outperforms the βSARMA and KARMA models except at the Kanyakumari location.

Neighborhood Disadvantage Increases Risk of Adverse Clinical Events in Children with Sickle Cell Disease

Background: Hydroxyurea is the most widely used pharmacologic agent to treat patients with sickle cell disease (SCD). Hydroxyurea treatment has well established effects of inducing expression of fetal hemoglobin (HbF) and a beneficial impact on clinical outcomes such as reduced number of vaso-occlusive (VOC) events, transfusions, and hospitalizations. In non-SCD populations, living in socio-economic disadvantage is a well-established factor for poor health outcomes. However, there is a paucity of data to describe how social stressors impact children with SCD. We hypothesized that socio-economic disadvantage impacts risk of adverse clinical outcomes in pediatric SCD patients even while on hydroxyurea therapy. Methods: We performed a retrospective chart review on 121 pediatric patients with severe SCD genotypes (homozygous HbS and sickle-beta 0 thalassemia) seen at Texas Children's Hospital (TCH) between 2010-2021. All patients were treated with hydroxyurea for a minimum of five years. Adherence to hydroxyurea was assessed through lab markers including absolute neutrophil count and reticulocyte counts. Patients not adherent were excluded from analysis. We examined the incidence of all clinical events for a total of 1026 patient years, including the number of office visits, ER visits, hospitalizations, transfusions, VOC, acute chest syndrome episodes (ACS), acute splenic sequestration (ASS), and febrile illness. We collected laboratory data including absolute neutrophil count, hemoglobin level, and HbF levels for each patient per year they were on hydroxyurea. We used the area deprivation index (ADI) to determine a score of neighborhood disadvantage amongst our cohort of patients. The ADI is a factor-based index which uses 17 US Census variables including poverty, education, and employment. We used individual residential addresses during our observation period to assign a geocode specific to each individual and obtain an ADI score. The ADI scores are ranked from 1-10, with higher ADI rankings reflecting a higher level of disadvantage. Results: All individuals with SCD had a robust response to hydroxyurea within their first year of initiating the drug (>20% HbF). We stratified our cohort based on their ADI scores into low ADI (1-3; n=42); medium ADI (4-6; n=42); and high ADI groups (7-10; n=37), where high ADI is the group with highest levels of disadvantage. All three groups had a similar average duration of hydroxyurea treatment. There were no significant differences in age, sex, or reason given for starting hydroxyurea between the ADI groups. When we examined hydroxyurea response, there was no significant difference in HbF levels at 1 year (23.8 vs. 24.06 %HbF in the low vs. high ADI groups) or after 5 years (19.6 vs. 18.6 % HbF in the low and high ADI groups). Individuals with high ADI did started hydroxyurea at a younger age (2.9 years vs. 4.9 years, p=0.02). We found that any individual living in an area with higher ADI had an increased incidence of adverse clinical events. We calculated the incidence of each clinical event per 100 patient years in our 3 ADI groups and used a conditional maximum likelihood estimate of rate ratio method to compare incidences (Table 1). We found that among individuals living in an area with a higher ADI (more deprived region), there was increased frequency of ER visits, hospitalizations, transfusions, VOC, and ASS. In particular, patients with the highest ADI had a 3 and 5 times higher rate of VOC and ASS, respectively (Table 1). Discussion: While we did not observe an association between ADI and HbF expression, our results show that higher neighborhood disadvantage is associated with poorer clinical outcomes among hydroxyurea-adherent pediatric patients with SCD who maintained a robust response to the drug (>20% HbF). All individuals in our study had a similar number of routine office visits at our clinic but any patient living in an area of high ADI had significantly more ER visits and hospitalizations for VOC and ASS events. While hydroxyurea is shown to reduce hospitalizations and VOC events in pediatric sickle cell patients, we show that neighborhood disadvantage can influence clinical outcomes even among patients who respond to hydroxyurea. More analysis remains in order to better characterize this association, and to understand additional strategies that can be used to reduce clinical events in pediatric patients of lower socioeconomic status.

Simultaneously Incomplete and Incoherent (SII) Dynamic LDV Models: With an Application to Financing Constraints and Firms’ Decision to Innovate

We develop novel methods for establishing coherency and completeness conditions in Static and Dynamic Limited Dependent Variables (LDV) Models. We characterize the two distinct problems as “empty-region” incoherency and “overlap-region” incoherency or incompleteness and show that the two properties can co-exist. We focus on the class of models that can be Simultaneously Incomplete and Incoherent (SII). We propose estimation strategies based on Conditional Maximum Likelihood Estimation (CMLE) for simultaneous dynamic LDV models without imposing recursivity. Point identification is achieved through sign-restrictions on parameters or other prior assumptions that complete the underlying data process. Using as modelling framework the Panel Bivariate Probit model with State Dependence, we analyse the impact of financing constraints on innovation: ceteris paribus, a firm facing binding finance constraints is substantially less likely to undertake innovation, while the probability that a firm encounters a binding finance constraint more than doubles if the firm is innovative. In addition, a strong role for state dependence in dynamic versions of our models is established.

Estimating item parameters in multistage designs with the tmt package in R

Various likelihood-based methods are available for the parameter estimation of item response theory models (IRT), leading to comparable parameter estimates. Considering multistage testing (MST) designs, Glas (1988; https://doi.org/10.2307/1164950) stated that the conditional maximum likelihood (CML) method in its original formulation leads to severely biased parameter estimates. A modified CML estimation method for MST designs proposed by Zwitser and Maris (2015; https://doi.org/10.1007/s11336-013-9369-6) finally provides asymptotically unbiased item parameter estimates. Steinfeld and Robitzsch (2021b; https://doi.org/10.31234/osf.io/ew27f) complemented this method to MST designs with probabilistic routing strategies. For both proposed modifications additional software solutions are required since design-specific information must be incorporated into the estimation process. An R package that has implemented both modifications is "tmt". In this article, first, the proposed solutions of the CML estimation in MST designs are illustrated, followed by the main part, the demonstration of the CML item parameter estimation with the R package "tmt". The demonstration includes the process of model specification, data simulation, and item parameter estimation, considering two different routing types of deterministic and probabilistic MST designs.

The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.

Conditional likelihood inference in a heteroscedastic functional measurement error model

In this paper, we deal with inference about the structural parameters in a heteroscedastic functional measurement error models under the normal distribution assumption. Given a minimal sufficient statistic for the incidental parameters, the conditional maximum likelihood (CML) approach is used. We show that CML estimators have explicit expressions and their sampling distribution is exact. We also show that the classical test statistics to test hypotheses of interest coincide and have exact distributions. We apply the statistical inference tools developed to a data set on comparison of measurement methods.

Autoregressive moving average model for matrix time series

In the paper, the autoregressive moving average model for matrix time series (MARMA) is investigated. The properties of the MARMA model are investigated by using the conditional least square estimation, the conditional maximum likelihood estimation, the projection theorem in Hilbert space and the decomposition technique of time series, which include necessary and sufficient conditions for stationarity and invertibility, model parameter estimation, model testing and model forecasting.