Related papers: Optimal sequential tests yield log-optimal e-proce…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
The win ratio is increasingly used in randomized trials due to its intuitive clinical interpretation, ability to incorporate the relative importance of composite endpoints, and its capacity for combining different types of outcomes (e.g.…
We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show…
Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, existing scaling methods have key limitations: parallel…
Sequential decision making significantly speeds up research and is more cost-effective compared to fixed-n methods. We present a method for sequential decision making for stratified count data that retains Type-I error guarantee or false…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
Process mining supports the analysis of the actual behavior and performance of business processes using event logs. % such as, e.g., sales transactions recorded by an ERP system. An essential requirement is that every event in the log must…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood…
In recent developments, a novel set of necessary optimality conditions for mixed constrained optimal control problems, termed the asymptotic weak maximum principle, has been formulated. These novel conditions deviate from the classical ones…
Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's…
In this article, we study the asymptotic behaviour of L\'evy processes with no positive jumps conditioned to stay positive. We establish integral tests for the lower envelope at 0 and at $+\infty$ and an analogue of Khintchin's law of the…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
Large computer networks are an essential part of modern technology, and quite often information needs to be broadcast to all the computers in the network. If all computers work perfectly all the time, this is simple. Suppose, however, that…
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
The superiority of stochastic symplectic methods over non-symplectic counterparts has been verified by plenty of numerical experiments, especially in capturing the asymptotic behaviour of the underlying solution process. How can one…
Large language models often improve reasoning by sampling multiple outputs and aggregating their final answers, but precise and efficient control of error levels remains a challenging task. In particular, deciding when to stop sampling…
We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic…