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Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…
Implicit functions such as Neural Radiance Fields (NeRFs), occupancy networks, and signed distance functions (SDFs) have become pivotal in computer vision for reconstructing detailed object shapes from sparse views. Achieving optimal…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…
The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity,…
When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide range of unseen scenarios, as well as for understanding the underlying mechanisms.…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
We extend a heuristic method for automatic dimensionality selection, which maximizes a profile likelihood to identify "elbows" in scree plots. Our extension enables researchers to make automatic choices of multiple hyper-parameters…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
We present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions (Robins (2004), Section 9; Li et al. (2004), Tchetgen et al. (2006),…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
We provide a semi-parametric analysis for the proportional likelihood ratio model, proposed by Luo & Tsai (2012). We study the tangent spaces for both the parameter of interest and the nuisance parameter, and obtain an explicit expression…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…