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This article proposes an approach to estimate and make inference on the parameters of copula link-based survival models. The methodology allows for the margins to be specified using flexible parametric formulations for time-to-event data, the baseline survival functions to be modeled using monotonic splines, and each parameter of the assumed joint survival distribution to depend on an additive predictor incorporating several types of covariate effects. All the model's coefficients as well as the smoothing parameters associated with the relevant components in the additive predictors are estimated using a carefully structured efficient and stable penalized likelihood algorithm. Some theoretical properties are also discussed. The proposed modeling framework is evaluated in a simulation study and illustrated using a real dataset. The relevant numerical computations can be easily carried out using the freely available GJRM R package. Supplementary materials for this article are available online.

Simultaneous state and parameter estimation is essential for control system design and dynamic modeling of physical systems. This capability provides critical real-time insight into system behavior, supports the discovery of underlying mechanisms, and facilitates adaptive control strategies. Surveyed in this review paper are two classes of state and parameter estimation methods: Kalman Filters and Luenberger Observers. The Kalman Filter framework, including its major variants such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Cubature Kalman Filter (CKF), and Ensemble Kalman Filter (EnKF), has been widely applied for joint and dual estimation in linear and nonlinear systems under uncertainty. In parallel, Luenberger observers, typically used in deterministic settings, offer alternative approaches through high-gain, sliding mode, and adaptive observer structures. This review focuses on the theoretical foundations, algorithmic developments, and application domains of these methods and provides a comparative analysis of their advantages, limitations, and practical relevance across diverse engineering scenarios.

Multi-modal sensor fusion has become ubiquitous in the field of vehicle motion estimation. Achieving a consistent sensor fusion in such a set-up demands the precise knowledge of the misalignments between the coordinate systems in which the different information sources are expressed. In ego-motion estimation, even sub-degree misalignment errors lead to serious performance degradation. The present work addresses the extrinsic calibration of a land vehicle equipped with standard production car sensors and an automotive-grade inertial measurement unit (IMU). Specifically, the article presents a method for the estimation of the misalignment between the IMU and vehicle coordinate systems, while considering the IMU biases. The estimation problem is treated as a joint state and parameter estimation problem, and solved using an adaptive estimator that relies on the IMU measurements, a dynamic single-track model as well as the suspension and odometry systems. Additionally, we show that the validity of the misalignment estimates can be assessed by identifying the misalignment between a high-precision INS/GNSS and the IMU and vehicle coordinate systems. The effectiveness of the proposed calibration procedure is demonstrated using real sensor data. The results show that estimation accuracies below 0.1 degrees can be achieved in spite of moderate variations in the manoeuvre execution.

While various data assimilation algorithms based on Bayes’ theorem have been developed for state estimation, some of these algorithms have also been applied to model parameter estimation. Coupled model parameter estimation (CPE) adjusts model parameters using available observations; then, the observation-adjusted parameters can greatly mitigate the model bias, which has great potential to reduce climate drift and enhance forecast skill in coupled climate models. However, given numerous model parameters that are associated with multiple time scales, how to conduct CPE with the simultaneous estimation of multiple parameters (SEMP) is still a popular research topic. With the aid of 3 coupled models, ranging from the conceptual coupled model to the intermediate coupled circulation model, this study has developed a systematic method to implement the SEMP–CPE. Linking coupled model sensitivities with the signal-to-noise ratio of the CPE, the SEMP–CPE method uses a timescale structure with coupled model sensitivities to determine which and how many parameters are estimated simultaneously in each CPE cycle to minimize the error of the coupled model simulation. Given that in a coupled model, the timescales by which different model components sensitively respond to a parameter perturbation can be quite different due to their different variabilities in their characteristic timescales, the first part of our study series focuses on the SEMP–CPE associated with single model component sensitivities. The results show that the quality of the model state analysis (in terms of assimilation) improves with the number of parameters being estimated by the order of sensitivities until the signal-to-noise ratio reaches a low threshold. Only when the most impactful physical parameters are estimated is the error of the state estimation consistently decreasing; as well as the signal-to-noise ratio in state-parameter covariance in SEMP scheme is enhanced. While only the signal extracted from the SEMP–CPE reaches saturated, the signal-to-noise ratio in the SEMP–CPE is maximized, and the state estimation error is minimized. Otherwise, if the parameters with low sensitivities are included in the CPE, the error of the state estimation increases instead. These results provide some insight into simultaneously estimating multiple parameters in a biased coupled general circulation model that assimilates real observations, which further improves climate analysis and prediction initialization.

A theory for approximate deconvolution and parameter estimation in certain infinite-dimensional linear dynamical systems with unbounded input and output is presented. The theory is exposed by frameworks for approximate parameter estimation and deconvolution in parabolic systems in discrete and continuous time with input and output on the boundary, and to delay systems with unbounded input and output, e.g. systems with delays in the input. Numerical results demonstrating the performance of the approximations are presented. Finally, the theory is applied to a data from transdermal alcohol model and sensor together with training data in the form of breath alcohol measurements to calibrate the sensor and approximately deconvolve blood alcohol content over time.

The parameter estimation of the nested logit model is conducted either simultaneously or sequentially. This is well known fact that the sequential method yields less efficient estimates than the simultaneous one, although its estimates are consistent and asymptotically efficient. Due to the computational burden, however, the sequential estimation is more often employed. Recently, the genetic algorithm has received a great deal of attention for its efficient solution for the nonconvex multidimensional problem. Generally, the parameter calibration of the nested logit model is nonconvex and hence, its solution may not be a global one. A hybrid estimation algorithm combining GA and the gradient method for the simultaneous nested logit model estimation has been suggested. The hybrid algorithm is implemented in a code, named G-Logit. An experimental test results, although limited, showed that the hybrid algorithm effectively search the solution domain of the nested logit model calibration and produced better estimates than the solely used gradient method.

This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

We propose a local measure of the relationship between parameter estimates and the moments of the data they depend on. Our measure can be computed at negligible cost even for complex structural models. We argue that reporting this measure can increase the transparency of structural estimates, making it easier for readers to predict the way violations of identifying assumptions would affect the results. When the key assumptions are orthogonality between error terms and excluded instruments, we show that our measure provides a natural extension of the omitted variables bias formula for nonlinear models. We illustrate with applications to published articles in several fields of economics.

We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic \"beta-min\" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.

This paper provides an overview of control function (CF) methods for solving the problem of endogenous explanatory variables (EEVs) in linear and nonlinear models. CF methods often can be justified in situations where \"plug-in\" approaches are known to produce inconsistent estimators of parameters and partial effects. Usually, CF approaches require fewer assumptions than maximum likelihood, and CF methods are computationally simpler. The recent focus on estimating average partial effects, along with theoretical results on nonparametric identification, suggests some simple, flexible parametric CF strategies. The CF approach for handling discrete EEVs in nonlinear models is more controversial but approximate solutions are available.