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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
A pairwise likelihood approach for the empirical estimati...
Nicolas Desassis, Didier Renard, Hélène Beucher, Sylvain Petitea · 2015-10-09 · via math.ST updates on arXiv.org

The plurigaussian model is particularly suited to describe categorical regionalized variables. Starting from a simple principle, the thresh-olding of one or several Gaussian random fields (GRFs) to obtain categories, the plurigaussian model is well adapted for a wide range ofsituations. By acting on the form of the thresholding rule and/or the threshold values (which can vary along space) and the variograms ofthe underlying GRFs, one can generate many spatial configurations for the categorical variables. One difficulty is to choose variogrammodel for the underlying GRFs. Indeed, these latter are hidden by the truncation and we only observe the simple and cross-variogramsof the category indicators. In this paper, we propose a semiparametric method based on the pairwise likelihood to estimate the empiricalvariogram of the GRFs. It provides an exploratory tool in order to choose a suitable model for each GRF and later to estimate its param-eters. We illustrate the efficiency of the method with a Monte-Carlo simulation study .The method presented in this paper is implemented in the R packageRGeostats.