相关论文: Student's $t$-test for scale mixture errors

The characterization of errors in a quantum system is a fundamental step for two important goals. First, learning about specific sources of error is essential for optimizing experimental design and error correction methods. Second,…

We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…

In a recent paper (Efron (2004)), Efron pointed out that an important issue in large-scale multiple hypothesis testing is that the null distribution may be unknown and need to be estimated. Consider a Gaussian mixture model, where the null…

The generalized quantum Stein's lemma characterizes the optimal asymptotic exponent of the type-II error in quantum hypothesis testing for an independent and identically distributed (IID) null hypothesis against a composite alternative…

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…

The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form…

Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to…

A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used…

The paper considers the classical Goodness of Fit test. It suggests to use the Gamma distribution for the approximation of the distribution of the Pearson statistics with unknown parameters estimated from raw data. The parameters of these…

Modern black-box predictive models are often accompanied by weak performance guarantees that only hold asymptotically in the size of the dataset or require strong parametric assumptions. In response to this, split conformal prediction…

We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…

Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…

To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary…

Researchers often rely on the t-statistic to make inference on parameters in statistical models. It is common practice to obtain critical values by simulation techniques. This paper proposes a novel numerical method to obtain an…

We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient…

Many inverse problems focus on recovering a quantity of interest that is a priori known to exhibit either discontinuous or smooth behavior. Within the Bayesian approach to inverse problems, such structural information can be encoded using…