Consistent Parameter Estimates Research Articles

Differentiable multi-ridge regression for system identification

Regularization aims to shrink model parameters, reducing complexity and overfitting risk. Traditional methods like LASSO and Ridge regression, limited by a single regularization hyperparameter, can restrict bias-variance trade-off adaptability. This paper addresses system identification in a multi-ridge regression framework, where an l2-penalty on the model coefficients is introduced, and a different regularization hyperparameter is assigned to each model parameter. To compute the optimal hyperparameters, a cross-validation-based criterion is optimized through gradient descent. Autoregressive and Output Error models are considered. The former requires formulating a regularized least-squares problem. The identification of the latter class is more challenging and is addressed by adopting regularized instrumental variable methods to ensure a consistent parameter estimation.

Understanding the Implications of a Complete Case Analysis for Regression Models with a Right-Censored Covariate

Despite its drawbacks, the complete case analysis is commonly used in regression models with incomplete covariates. Understanding when the complete case analysis will lead to consistent parameter estimation is vital before use. Our aim here is to demonstrate when a complete case analysis is consistent for randomly right-censored covariates and to discuss the implications of its use even when consistent. Across the censored covariate literature, different assumptions are made to ensure a complete case analysis produces a consistent estimator, which leads to confusion in practice. We make several contributions to dispel this confusion. First, we summarize the language surrounding the assumptions that lead to a consistent complete case estimator. Then, we show a unidirectional hierarchical relationship between these assumptions, which leads us to one sufficient assumption to consider before using a complete case analysis. Lastly, we conduct a simulation study to illustrate the performance of a complete case analysis with a right-censored covariate under different censoring mechanism assumptions, and we demonstrate its use with a Huntington disease data example.

A global test for heteroscedastic one-way FMANOVA with applications

Multivariate functional data are prevalent in various fields such as biology, climatology, and finance. Motivated by the World Health Data applications, in this study, we propose and examine a global test for assessing the equality of multiple mean functions in multivariate functional data. This test addresses the one-way Functional Multivariate Analysis of Variance (FMANOVA) problem, which is a fundamental issue in the analysis of multivariate functional data. While numerous analysis of variance tests have been proposed and studied for univariate functional data, only a limited number of methods have been developed for the one-way FMANOVA problem. Furthermore, our global test has the ability to handle heteroscedasticity in the unknown covariance function matrices that underlie the multivariate functional data, which is not possible with existing methods. We establish the asymptotic null distribution of the test statistic as a chi-squared-type mixture, which depends on the eigenvalues of the covariance function matrices. To approximate the null distribution, we introduce a Welch–Satterthwaite type chi-squared-approximation with consistent parameter estimation. The proposed test exhibits root-n consistency, meaning it possesses nontrivial power against a local alternative. Additionally, it offers superior computational efficiency compared to several permutation-based tests. Through simulation studies and applications to the World Health Data, we highlight the advantages of our global test.

Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations

The object of investigation is the mixed fractional Brownian motion of the form ${X_{t}}=\kappa {B_{t}^{{H_{1}}}}+\sigma {B_{t}^{{H_{2}}}}$, driven by two independent fractional Brownian motions ${B_{1}^{H}}$ and ${B_{2}^{H}}$ with Hurst parameters ${H_{1}}\lt {H_{2}}$. Strongly consistent estimators of unknown model parameters ${({H_{1}},{H_{2}},{\kappa ^{2}},{\sigma ^{2}})^{\top }}$ are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for $0\lt {H_{1}}\lt {H_{2}}\lt \frac{3}{4}$.

CenTime: Event-conditional modelling of censoring in survival analysis

Survival analysis is a valuable tool for estimating the time until specific events, such as death or cancer recurrence, based on baseline observations. This is particularly useful in healthcare to prognostically predict clinically important events based on patient data. However, existing approaches often have limitations; some focus only on ranking patients by survivability, neglecting to estimate the actual event time, while others treat the problem as a classification task, ignoring the inherent time-ordered structure of the events. Additionally, the effective utilisation of censored samples−data points where the event time is unknown− is essential for enhancing the model’s predictive accuracy. In this paper, we introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. We demonstrate that our approach forms a consistent estimator for the event model parameters, even in the absence of uncensored data. Furthermore, CenTime is easily integrated with deep learning models with no restrictions on batch size or the number of uncensored samples. We compare our approach to standard survival analysis methods, including the Cox proportional-hazard model and DeepHit. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance. Our implementation is publicly available at https://github.com/ahmedhshahin/CenTime.

Factors of Using Long Acting and Permanent Methods (LAPM) of Contraception: Bangladesh Perspective

The Government of Bangladesh is very much aware of controlling excessive birth rate to maintain population problem. Though Bangladesh is owning self-sufficiency in many sectors, the increasing population is a great impediment for the development of the country. So, promoting different contraceptive methods is of much importance. This work aims at identifying the important determinants that affect the long-acting and permanent methods (LAPM) of contraception. Firstly, chi-square test of association is carried out for defining the correlates of LAPM of contraception using Bangladesh Demographic and Health Survey (BDHS), 2017-18 data. For estimating the effects of each controlled independent variables, data are further analyzed within a multivariate framework. To obtain consistent and efficient estimates of parameters of interest, multinomial logistic regression model is used in this work. The study finds several socio-economic and demographic variables having high impact on using LAPM. The study findings are properly discussed and recommendations are made accordingly for the policy makers.
 Dhaka Univ. J. Sci. 71(2): 87-94, 2023 (July)

The nonlinear impacts of aging labor and government health expenditures on productivity in ASEAN+3 economies

The aging of the workforce has become a paramount concern for ASEAN+3’s productivity. In response, government health expenditure emerges as a potential solution. However, the existing literature has generated inconclusive results and has yet to reveal the mechanisms and potential nonlinear effects of these factors on productivity. This study addresses this gap by examining the impact of changes in the proportion of the working-age population and government health expenditures on productivity growth, using data from ASEAN+3 countries over the period 2008–2009. Employing a robust methodology, we utilize several panel threshold regression models to derive statistically sound inferences and consistent parameter estimates. Our investigation reveals that government health expenditure effectively enhances productivity when the old labor force participation rate is below 51.352%. However, this effect loses significance at higher levels of the aging workers’ proportion. Additionally, we identify an optimal government health expenditure range of 1.906% to 2.859% of GDP, signifying a positive correlation with labor productivity growth.

Linear panel regressions with two-way unobserved heterogeneity

We study linear panel regression models in which the unobserved error term is an unknown smooth function of two-way unobserved fixed effects. In standard additive or interactive fixed effect models the individual specific and time specific effects are assumed to enter with a known functional form (additive or multiplicative). In this paper, we allow for this functional form to be more general and unknown. We discuss two different estimation approaches that allow consistent estimation of the regression parameters in this setting as the number of individuals and the number of time periods grow to infinity. The first approach uses the interactive fixed effect estimator in Bai (2009), which is still applicable here, as long as the number of factors in the estimation grows asymptotically. The second approach first discretizes the two-way unobserved heterogeneity (similar to what Bonhomme et al., 2021 are doing for one-way heterogeneity) and then estimates a simple linear fixed effect model with additive two-way grouped fixed effects. For both estimation methods we obtain asymptotic convergence results, perform Monte Carlo simulations, and employ the estimators in an empirical application to UK house price data.

Asymptotic Normality of Parameter Estimators for~Mixed Fractional Brownian Motion with Trend

We investigate the mixed fractional Brownian motion of the form Xt = θt+σWt +κBtH , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (θ, H, σ, κ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 12 ).

Analysis of Multivariate Survival Data under Semiparametric Copula Models

AbstractModelling multivariate survival data is complicated by the complex association structure among the responses. To balance model flexibility and interpretability, we propose a semiparametric copula model to modulate multivariate survival data, with the marginal distributions of the response components described by semiparametric linear transformation models. To conduct inference about the model parameters, we develop a two‐stage maximum likelihood method and a three‐stage pseudo‐likelihood estimation procedure. We investigate the impact of model misspecification on the estimation of covariate effects and identify a scenario in which consistent estimation of the marginal parameters is retained even when the copula model is misspecified. The proposed methods are justified both theoretically and empirically. An application to a real dataset is provided to demonstrate the utility of the proposed method.

Analysis of World Economic Growth Using Panel Data

In this paper, I consider panel data analysis of world economies to identify the relationship between GDP growth and the independent variables, and the nature of effect that may exist. Annual data for 161 countries from 1990 to 2020 sourced from the World Bank and UN are used. GDP is the independent variable while the independent variables are population, gross value added, total natural resources rent, and labor force. Firstly, a poolability test is performed to test for the joint significance of the fixed effects. The null hypothesis is rejected as there exist significant individual effects. Secondly, Huesman’s test is performed to test for consistency of fixed effect and random effect. The null hypothesis is rejected implying significant random effects exist. Thirdly, Bruesch-Pagan test for heteroscedasticity is performed, which shows the existence of heteroscedasticity. Finally, White’s covariance matrix estimator for random effect is performed which results to consistent and efficient parameter estimate in the presence of heteroscedasticity. The random effect model is statistically significant at the 5% level, with 68 % of the variation being explained by the model. All the explanatory variables are statistically significant at a 5 % level. They all have a positive effect on GDP with the labor force and population having the highest effect. The random effect is large and significant with a variance of 2.25±1.5 and 94.1 % share of the error component. Countries that have had consistent increases in either labor force or population growth or both, has over the period experienced consistent economic growth after controlling for the other variables and the random effect.

SPECIFICATION ANALYSIS OF STRUCTURAL CREDIT RISK MODEL WITH STOCHASTIC VOLATILITY

In this research, we conduct specification analysis of structural credit risk models with stochastic volatility using term structure of Credit Default Swap (CDS) spreads and equity volatility form high-frequency return data. We also test five representatives of structural credit risk models using samples of 93 single name CDS contracts from January 2010 -2022. The model we consider are; the standard Merton(1974) model, the Black & Cox (1976) model with flat barrier, the Longstaff and Schwartz(1995)model with stochastic interest rates, the Collin- Dufresne and Goldstein (2001) model with stationary leverage, and the double exponential jump diffusion model used in Huang & Huang(2003). Our study provides consistent econometric estimation of the pricing model parameters and specification tests based on the joint behavior of time-series asset dynamics and cross-sectional pricing errors. Our empirical tests reject strongly the standard Merton (1974) model, the Black and Cox (1976) with flat barrier model, the Longstaff, Schwartz (1995) model with stochastic interest rates. The double exponential jump-diffusion barrier model used in (Huang and Huang, 2003) improves significantly over the five models. The best model is the stationary leverage model of Collin-Dufresne and Goldstein (2001), which we cannot reject at 0.5 level of significance in our sample firm. However, our empirical results document the inability of the existing structural models to capture the dynamic behavior of CDS spreads and equity volatility, especially for high investment grade names derivatives. These points to a potential role of time-varying asset volatility, a feature that is missing in the standard structural models.

Consistently estimating network statistics using aggregated relational data

Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which ask respondents questions of the form "How many people with trait X do you know?" provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collect the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization by deriving conditions under which statistics about the unobserved network (or functions of these statistics like regression coefficients) can be consistently estimated using ARD. We first provide consistent estimates of network model parameters for three commonly used probabilistic models: the beta-model with node-specific unobserved effects, the stochastic block model with unobserved community structure, and latent geometric space models with unobserved latent locations. A key observation is that cross-group link probabilities for a collection of (possibly unobserved) groups identify the model parameters, meaning ARD are sufficient for parameter estimation. With these estimated parameters, it is possible to simulate graphs from the fitted distribution and analyze the distribution of network statistics. We can then characterize conditions under which the simulated networks based on ARD will allow for consistent estimation of the unobserved network statistics, such as eigenvector centrality, or response functions by or of the unobserved network, such as regression coefficients.

Development of the grass LAI and CCC remote sensing-based models and their transferability using sentinel-2 data in heterogeneous grasslands

ABSTRACT Estimation of biophysical variables such as leaf area index (LAI) and canopy chlorophyll content (CCC) at high spatiotemporal resolution is important for managing natural and heterogeneous environments. However, accurate estimation of biophysical variables particularly over heterogeneous environments remains a challenge. The objective of the study was to develop locally parameterized grass LAI and CCC empirical models using the Sentinel-2 variables combined with the Stepwise multiple linear regression (SMLR) and Random forest (RF) at the Golden Gate Highlands National Park (GGHNP) and Marakele National Park (MNP) in South Africa. Results showed that in MNP, SMLR yielded better LAI estimation with root mean squared error (RMSE) of 0.67 m2.m−2 and mean adjusted error (MAE) of 0.54, explaining 48% of LAI variability, when bands and indices are combined. In contrast, RF gave better CCC estimation i.e. RMSE and MAE of 17.08 µg.cm−2 and 13.18 respectively, explaining about 40% of CCC variability with Sentinel-2 bands only. In GGHNP, the RF models provided the best estimates of both LAI and CCC compared to SMLR models. Furthermore, the CCC and LAI estimation models of GGHNP showed improved model accuracies when 50% and 75% of the MNP field samples were transferred to the GGHNP models. In contrast, the CCC and LAI estimation models of MNP showed a decline in model performance across all scenarios where the GGHNP field samples were transferred to the MNP models. These findings have significant implications for the development of locally parameterized types of models that can provide improved and consistent site-specific accurate estimates of grass biophysical parameters over heterogeneous environments.

Consistent Subspace Identification of Errors-in-Variables Hammerstein Systems

In this article, a consistent subspace identification method (SIM) is proposed for block-oriented errors-in-variables Hammerstein systems. Due to that the existing SIMs using parity subspace based on noisy measurements may result in biased parameter estimates, we propose a scheme for the consistent system parameter estimation, which estimates the noise-free Hankel matrix using available noisy measurements and noise variances. A 2-D search method is proposed to estimate the unknown noise variances from available noisy measurements. After that consistent estimations of the Hammerstein system parameters can be then retrieved from the estimated noise-free Hankel matrix following the same algorithm framework of the existing SIMs using parity subspace. Two simulation examples are included to support the effectiveness and merits of the proposed method.

Fast estimation of mixed-effects location-scale regression models.

As a result of advances in data collection technology and study design, modern longitudinal datasets can be much larger than they historically have been. Such "intensive" longitudinal datasets are rich enough to allow for detailed modeling of the variance of a response as well as the mean, and a flexible class of models called mixed-effects location-scale (MELS) regression models are commonly used to do so. However, fitting MELS models can pose computational challenges related to the numerical evaluation of multi-dimensional integrals; the slow runtime of current methods is inconvenient for data analysis and makes bootstrap inference impractical. In this paper, we introduce a new fitting technique, called FastRegLS, that is considerably faster than existing techniques while still providing consistent estimators for the model parameters.

CONSISTENT NON-GAUSSIAN PSEUDO MAXIMUM LIKELIHOOD ESTIMATORS OF SPATIAL AUTOREGRESSIVE MODELS

This paper studies the non-Gaussian pseudo maximum likelihood (PML) estimation of a spatial autoregressive (SAR) model with SAR disturbances. If the spatial weights matrix $M_{n}$ for the SAR disturbances is normalized to have row sums equal to 1 or the model reduces to a SAR model with no SAR process of disturbances, the non-Gaussian PML estimator (NGPMLE) for model parameters except the intercept term and the variance $\sigma _{0}^{2}$ of independent and identically distributed (i.i.d.) innovations in the model is consistent. Without row normalization of $M_{n}$ , the symmetry of i.i.d. innovations leads to consistent NGPMLE for model parameters except $\sigma _{0}^{2}$ . With neither row normalization of $M_{n}$ nor the symmetry of innovations, a location parameter can be added to the non-Gaussian pseudo likelihood function to achieve consistent estimation of model parameters except $\sigma _{0}^{2}$ . The NGPMLE with no added parameter can have a significant efficiency improvement upon the Gaussian PML estimator and the generalized method of moments estimator based on linear and quadratic moments. We also propose a non-Gaussian score test for spatial dependence, which can be locally more powerful than the Gaussian score test. Monte Carlo results show that our NGPMLE with no added parameter and the score test based on it perform well in finite samples.

Statistics of the two star ERGM

In this paper, we explore the two star Exponential Random Graph Model, which is a two parameter exponential family on the space of simple labeled graphs. We introduce auxiliary variables to express the two star model as a mixture of the β model on networks. Using this representation, we study asymptotic distribution of the number of edges, and the sampling variance of the degrees. In particular, the limiting distribution for the number of edges has similar phase transition behavior to that of the magnetization in the Curie-Weiss Ising model of Statistical Physics. Using this, we show existence of consistent estimates for both parameters. Finally, we prove that the centered partial sum of degrees converges as a process to a Brownian bridge in all parameter domains, irrespective of the phase transition.

Conditional predictive inference for stable algorithms

We investigate generically applicable and intuitively appealing prediction intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response pairs are omitted. Our results are based on a finite sample analysis of the empirical distribution function of k-fold cross-validation residuals and hold in nonparametric settings with only minimal assumptions on the error distribution. To illustrate our results, we also apply them to high-dimensional linear predictors, where we obtain uniform asymptotic training conditional validity as both sample size and dimension tend to infinity at the same rate and consistent parameter estimation typically fails. These results show that despite the serious problems of resampling procedures for inference on the unknown parameters (cf. in A Festschrift for Erich L. Lehmann (1983) 28–48 Wadsworth; Ann. Statist. 24 (1996) 307–335; J. Mach. Learn. Res. 19 (2018) 5), cross-validation methods can be successfully applied to obtain reliable predictive inference even in high dimensions and conditionally on the training data.

Challenges to the air cargo business of combination carriers: Analysis of two major Korean Airlines

This research explores the efficiency and the total factor productivity of the air cargo business of combination carriers (CCs) using stochastic frontier production. The authors estimate the coefficients of the two models by applying operational data and environment variables. We develop a single-step maximum likelihood procedure to obtain consistent parameter estimates and identify determinants of two airlines’ technical efficiency. We found that the air cargo business of CCs with cargo-dedicated aircraft (CDA) is at stake, shrinking their activities, rate, yield, economies of scale, density, and productivity. The CCs with CDA should update the air cargo business model to reflect current trends. Collaboration is recommended to balance supply and demand and reduce the dissimilarities between passenger and cargo transport businesses.