Related papers: Locally most powerful sequential tests of a simple…
While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…
We propose a general framework for constructing powerful, sequential hypothesis tests for a large class of nonparametric testing problems. The null hypothesis for these problems is defined in an abstract form using the action of two known…
Suppose that we have two training sequences generated by parametrized distributions $P_{\theta^*}$ and $P_{\xi^*}$, where $\theta^*$ and $\xi^*$ are unknown true parameters. Given training sequences, we study the problem of classifying…
In multigroup data settings with small within-group sample sizes, standard $F$-tests of group-specific linear hypotheses can have low power, particularly if the within-group sample sizes are not large relative to the number of explanatory…
In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables, with expectation $p$ under $\mathcal{H}_0$…
Identifying the most powerful test in multiple hypothesis testing under strong family-wise error rate (FWER) control is a fundamental problem in statistical methodology. State-of-the-art approaches formulate this as a constrained…
Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus…
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…
Suppose $\widehat\theta_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be respectively the last $n$ and the total number of $n$ for which $\widehat\theta_n$ is at least…
Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness…
We study the optimal multiple stopping time problem defined for each stopping time $S$ by $v(S)=\operatorname {ess}\sup_{\tau_1,...,\tau_d\geq S}E[\psi(\tau_1,...,\tau_d)|\mathcal{F}_S]$. The key point is the construction of a new reward…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error…
The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…