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When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Context: Conducting experiments is central to research machine learning research to benchmark, evaluate and compare learning algorithms. Consequently it is important we conduct reliable, trustworthy experiments. Objective: We investigate…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
An association rule is statistically significant, if it has a small probability to occur by chance. It is well-known that the traditional frequency-confidence framework does not produce statistically significant rules. It can both accept…
Subsampling is a general statistical method developed in the 1990s aimed at estimating the sampling distribution of a statistic $\hat \theta _n$ in order to conduct nonparametric inference such as the construction of confidence intervals…
This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
Whereas confidence intervals are used to assess uncertainty due to unmeasured individuals, confounding intervals can be used to assess uncertainty due to unmeasured attributes. Previously, we have introduced a methodology for computing…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
We propose the use of a simple intuitive principle for measuring algorithmic classification bias: the significance of the differences in a classifier's error rates across the various demographics is inversely commensurate with the sample…
Detecting and locating changes in highly multivariate data is a major concern in several current statistical applications. In this context, the first contribution of the paper is a novel non-parametric two-sample homogeneity test for…
We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…
Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…
Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…
We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic…