Related papers: Asymptotics in randomized urn models
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
An urn contains balls of d colors. At each time, a ball is drawn and then replaced together with a random number of balls of the same color. Assuming that some colors are dominated by others, we prove central limit theorems. Some…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
Randomization is a common technique used in clinical trials to eliminate potential bias and confounders in a patient population. Equal allocation to treatment groups is the standard due to its optimal efficiency in many cases. However, in…
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The Urn Model with…
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…
An extended Polya urn Model with two colors, black and white, is studied with some SLLN and CLT on the proportion of white balls.
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
Typically, a randomized experiment is designed to test a hypothesis about the average treatment effect and sometimes hypotheses about treatment effect variation. The results of such a study may then be used to inform policy and practice for…
This paper concerns the long term behaviour of a growth model describing a random sequential deposition of particles on a finite graph. The probability of allocating a particle at a vertex is proportional to a log-linear function of numbers…
We use the holonomic ansatz to estimate the asymptotic behavior, in $T$, of the average maximal number of balls in a bin that is obtained when one throws uniformly at random (without replacement) $r$ balls into $n$ bins, $T$ times. Our…
We examine study designs for extending (generalizing or transporting) causal inferences from a randomized trial to a target population. Specifically, we consider nested trial designs, where randomized individuals are nested within a sample…
Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference…
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
This paper considers endogenous selection models, in particular nonparametric ones. Estimating the unconditional law of the outcomes is possible when one uses instrumental variables. Using a selection equation which is additively separable…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.
We introduce a class of reinforcement models where, at each time step $t$, one first chooses a random subset $A_t$ of colours (independent of the past) from $n$ colours of balls, and then chooses a colour $i$ from this subset with…