Tadeusz Inglot
We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all unbounded densities. We give a sufficient condition under which MD theorem holds. The proof is based on Mogulskii's inequality.
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Neyman and Pearson's theory of testing hypotheses does not warrant minimal epistemic reliability: the feature of driving to true conclusions more often than to false ones. The theory does not protect from the possible negative effects of the pragmatic value-laden unequal setting of error probabilities on the theory's epistemic reliability. Most importantly, in the case of a negative impact, no methodological adjustment is available to neutralize it, so in such cases, the discussed pragmatic-value-ladenness of the theory inevitably compromises the goal of attaining truth.
How e-values generalize hypothesis testing: a Neyman-Pearson lemma for the e-value
该研究构建统一决策论框架，将e值视为假设检验的多决策推广，推导了e值的Neyman-Pearson引理，还得到无假设的复合零假设经典Neyman-Pearson引理，明确了e值与经典假设检验的关系。
Bounding Neyman-Pearson Region with $f$-Divergences
本文研究二元假设检验的 Neyman-Pearson 区域边界，利用任意 $f$-散度给出最优下界，并基于 Chernoff $α$-系数获得闭式上界及实现边界的分布构造方法。
We point out that the Neyman-Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximises the expected power for a fixed expected type-1 error rate. For Bayes factors involving a simple null hypothesis, the expected type-1 error rate is just the completely frequentist type-1 error rate. Lastly we remark on connections between the Karlin-Rubin theorem and uniformly most powerful tests, and Bayes factors. This provides frequentist motivations for computing the Bayes factor and could help reconcile Bay…
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specified level and (ii), it has probability of type II error close to the minimum possible. The proposed classifier is obtained by solving an optimization problem with an empirical objective and an empirical co…
Despite frequent calls for the overhaul of null hypothesis significance testing (NHST), this controversial procedure remains ubiquitous in behavioral, social and biomedical teaching and research. Little change seems possible once the procedure becomes well ingrained in the minds and current practice of researchers; thus, the optimal opportunity for such change is at the time the procedure is taught, be this at undergraduate or at postgraduate levels. This paper presents a tutorial for the teaching of data testing procedures, often referred to as hypothesis testing theories. The first procedure…
The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). This paradigm is suitable for applications such as severe disease diagnosis, fraud detection, among others. A series of NP classifiers have been developed to guarantee the type I error control with high probability. However, these existing classifiers involve a sample splitting step: a mixture of class 0 and class 1 observations to construct a scoring function and some left-out class 0 observations…
Optimal Decision Rules for Composite Binary Hypothesis Testing under Neyman-Pearson Framework
本文研究Neyman-Pearson框架下复合二元假设检验，通过广义贝叶斯规则实现最优功效，推导简单原假设下的加权似然比单阈值规则，并扩展到复合原假设及平均/最坏虚警约束，给出指数族实例验证。
This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an N-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of …
Tightening Control in Neyman--Pearson Linear Classification
研究奈曼 - 皮尔逊分类框架下的统计学习，针对其复杂性及有限样本控制约束问题，提出两种精度控制策略下的改进学习程序及相关预测推断方法，模拟显示有限样本性能良好。
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different Hölder Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size $n$ goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially…
The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $α$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types. Recently, Tong, Feng and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error…
In fields that are mainly nonexperimental, such as economics and finance, it is inescapable to compute test statistics and confidence regions that are not probabilistically independent from previously examined data. The Bayesian and Neyman-Pearson inference theories are known to be inadequate for such a practice. We show that these inadequacies also hold m.a.e. (modulo approximation error). We develop a general econometric theory, called the neoclassical inference theory, that is immune to this inadequacy m.a.e. The neoclassical inference theory appears to nest model calibration, and most econ…
We show that for local alternatives which are not square integrable the intermediate (or Kallenberg) efficiency of the Neyman-Pearson test for uniformity with respect to the classical Kolmogorov-Smirnov test is equal to infinity. Contrary to this, for local square integrable alternatives the intermediate efficiency is finite and can be explicitly calculated.
Chi-squared tests for lack of fit are traditionally employed to find evidence against a hypothesized model, with the model accepted if the Karl Pearson statistic comparing observed and expected numbers of observations falling within cells is not significantly large. However, if one really wants evidence for goodness of fit, it is better to adopt an equivalence testing approach in which small values of the chi-squared statistic are evidence for the desired model. This method requires one to define what is meant by equivalence to the desired model, and guidelines are proposed. Then a simple exte…
Towards a unified theory for testing statistical hypothesis: Multinormal mean with nuisance covariance matrix
本文研究含未知协方差矩阵的多元正态均值受限备择检验，提出调和贝叶斯、Fisher、Neyman-Pearson 与 Wald 理论的框架，并揭示 LRT/UIT 的 α-不容许性。
Conformal Prediction Through the Lens of Hypothesis Testing: Universality, Impossibility, and Optimality
本文从可交换性原假设的置换检验视角阐释共形预测，借助经典假设检验理论重现共形预测的普适性与不可能性结果，并推导得出最优共形预测器的形式。
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