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Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
We use location model methodology to guide the least squares analysis of the Lasso problem of variable selection and inference. The nuisance parameter is taken to be an indicator for the selection of explanatory variables and the interest…
Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…
We propose a novel statistical method for testing the results of anomaly detection (AD) under domain adaptation (DA), which we call CAD-DA -- controllable AD under DA. The distinct advantage of the CAD-DA lies in its ability to control the…
G-computation has become a widely used robust method for estimating unconditional (marginal) treatment effects with covariate adjustment in the analysis of randomized clinical trials. Statistical inference in this context typically relies…
Determining whether an algorithmic decision-making system discriminates against a specific demographic typically involves comparing a single point estimate of a fairness metric against a predefined threshold. This practice is statistically…
The Coordinate Ascent Variational Inference scheme is a popular algorithm used to compute the mean-field approximation of a probability distribution of interest. We analyze its random scan version, under log-concavity assumptions on the…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…
Binary endpoints are common in clinical trials and conditional odds ratios have traditionally been used to assess treatment effects. However, the interpretation of odds ratios is difficult, they are non-collapsible and rely on strong…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
High-dimensional regression models with regularized sparse estimation are widely applied. For statistical inferences, debiased methods are available about single coefficients or predictions with sparse new covariate vectors (also called…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…