45 problems

Piecewise Convex Information Criterion conjecture. PCIC consistently selects the number of convexity change points and is asymptotically efficient within the class of methods that…

The data consist of $n=2809$ genes measured under $d=19$ conditions, with an interaction model describing gene profiles across conditions. Biologists' conjecture. If the interactio…

Let model selection mean adaptive selection of nonzero means, and let the underlying estimand be $bc$, belonging to one of the parameter spaces and considered under one of the loss…

The paper considers model selection using plug-in codes, which code each new outcome using a distribution indexed by the maximum-likelihood estimator based on preceding outcomes. P…

Voronoi-loss conjecture. The novel loss should satisfy

Let $\mathcal{V}$ be the unrestricted model space, let an informed Metropolis–Hastings sampler assign proposal probabilities in its neighborhood according to the target posterior p…

Let $\hat{k}_T$ be the model selected by simple validation, let $k_*$ denote the oracle model index, and let $\Delta$ be the scale factor from Definition 3.defodgs. Local order con…

Optimal linear aggregation rates conjecture. The proposed approach can attain the optimal $K/n$ rates for linear density aggregation in the observational case.

Let MCMs be minimally complex models formed as the union of independent irreducible correlation components, and consider spin models with the same number of parameters and the same…

A model-selection procedure chooses among a collection of models $\mathcal{M}$, and a large collection of models is one whose richness can substantially increase the minimal penalt…

MHDAIC prediction-rate conjecture. The quantity

Let $\hat{\theta}_{\Pi}$ denote the least squares estimator associated with a model or cone indexed by $\Pi$. In the model-selection setting for piecewise monotone signals, one see…

Let $\operatorname{pen}_{\mathrm{opt}}^{\mathrm{gal}}(m)$ be the optimal penalty and suppose that Algorithms 5–6 are first-order optimal for a model-selection problem. Let…

Let Algorithms 5–6 be the minimal-penalty procedures applied to a collection of candidate estimators, and consider estimator-selection problems beyond the few settings for which co…

Consider penalized least-squares change-point detection, with model dimension $D_m$, sample size $n$, and a minimal penalty and optimal penalty for selecting the change-point model…

Consider statistical settings with an estimator collection $(\widehat{s}_m)_{m\in\mathcal{M}}$, a complexity measure $\mathcal{C}_m$, and minimal-penalty algorithms based on a pena…

Let $\mathcal{M}$ be a collection of models, let $\widehat{s}_m$ be the estimator associated with $m\in\mathcal{M}$, and let $\mathcal{R}$ and $\widehat{\mathcal{R}}_n$ denote the…

HIW-prior extension conjecture. The consistency results continue to hold for a general HIW prior.

The model-selection setting involves an estimator $\hat{d}_{VC}$ of the VC dimension $d_{VC}$, with convergence measured in probability. The existing result gives only a rate of or…

Let $K$ be the number of convexity change points, let $p$ be the number of knots, and define the Piecewise Convex Information Criterion by … Here the default values are…

Suppose the number of change points is unknown, and augment the estimation criterion by a penalty proportional to $\ln(N)$ times the number of change points. This produces the piec…

Irrepresentability conjecture. In linear regression models under irrepresentability conditions on the design matrix, one may take $T=S_0$. This would mean that no variables outside…

Consider Yang's setting of model selection between two nested linear regression models with fixed design and Gaussian errors of fixed variance, where risk is measured by the in-mod…

Let $S$ denote the model-support variable in the empirical Bayes prior, and consider priors on $S$ that yield the minimax posterior concentration rate under prediction error loss.…

Alternative quasi-likelihood conjecture. Similar Bayesian asymptotic properties for model selection should be derivable for these alternative quasi-likelihoods.