Testing the number of parameters with multidimensional MLP

Understanding Weight Similarity of Neural Networks via Chain Normalization Rule and Hypothesis-Training-Testing

We present a weight similarity measure method that can quantify the weight similarity of non-convex neural networks. To understand the weight similarity of different trained models, we propose to extract the feature representation from the weights of neural networks. We first normalize the weights of neural networks by introducing a chain normalization rule, which is used for weight representation learning and weight similarity measure. We extend the traditional hypothesis-testing method to a hypothesis-training-testing statistical inference method to validate the hypothesis on the weight simi…

Heteroscedastic semiparametric transformation models: estimation and testing for validity

In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is independent of the multidimensional covariates. In this model, we first consider the estimation of the unknown components of the model, namely the transformation parameter, regression and variance function and the distribution of the error. We show the asymptotic normality of the proposed estimators. Second, we propose tests for the validity of the model, and es…

面向高维数据的配对样本假设检验框架

A framework for paired-sample hypothesis testing for high-dimensional data

针对高维配对样本检验，本文提出基于实例对垂直平分超平面与 Hodges–Lehmann 聚合规则生成一维评分，并用 Wilcoxon 符号秩检验的两步框架，提升准确率且可解释特征贡献。

顺序多重检验：二阶渐近分析

Sequential Multiple Testing: A Second-Order Asymptotic Analysis

本文提出二阶渐近最优理论，证明了多个已知第一阶最优的顺序多重检验程序在二阶条件下同样最优，并推导了最小样本量的二阶修正项。

多维扩散过程的稳健推断方法

Robust Inferential Methodology for Multidimensional Diffusion Processes

本文提出基于最小密度幂分歧估计器的稳健参数估计与检验方法，用于高频观测的多维扩散过程，证明了参数估计的一致性和渐近正态性，并展示了其在处理异常值和模型不准确时的鲁棒性。

Estimation and testing for multiple regulation of multivariate mixed outcomes

Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of related disorders. We seek to identify {\em multiple regulators} or predictors that are associated with multiple outcomes when these outcomes may be measured on very different scales or composed of a mixture of continuous, binary, and not-fully-observed elements. We first propose an estimation technique to put all effects on similar scales, and we induce spar…

Testing for common arrivals of jumps for discretely observed multidimensional processes

We consider a bivariate process $X_t=(X^1_t,X^2_t)$, which is observed on a finite time interval $[0,T]$ at discrete times $0,Δ_n,2Δ_n,....$ Assuming that its two components $X^1$ and $X^2$ have jumps on $[0,T]$, we derive tests to decide whether they have at least one jump occurring at the same time ("common jumps") or not ("disjoint jumps"). There are two different tests for the two possible null hypotheses (common jumps or disjoint jumps). Those tests have a prescribed asymptotic level, as the mesh $Δ_n$ goes to 0. We show on some simulations that these tests perform reasonably well even in…

Multivariate inhomogeneous diffusion models with covariates and mixed effects

Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges parameter inference and approximations are inevitable. We propose a method for approximate maximum-likelihood parameter estimation in multivariate time-inhomogeneous diffusions, where subject-specific flexibility is accounted for by incorporation of multidimensional mixed effects and covariates. We consider $N$ multidimensional independent diffusions $X^i = (X…

检验多维伊藤半鞅的现货协方差矩阵的秩

Testing the rank of the spot covariance matrix of a multidimensional Itô semi-martingale

利用高频观测开发统计检验，针对多维伊藤半鞅现货协方差矩阵最大秩，通过重新中心化协方差估计器考虑适应漂移，检验原假设，导出临界值，分析功效，模拟结果显示该检验比经典方法功效更高。

Estimation and Test for Multidimensional Regression Models

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator. We show in this paper that if we choose to minimise the logarithm of the determinant of the empirical error covariance matrix, then we get an asymptotically optimal estimator. Moreover, under suitable assumptions, we show that this cost function leads to a very simple asymptotic law for testing the number of parameters of an identi…

A Unifying Framework for Adaptive Radar Detection in Homogeneous plus Structured Interference-Part I: On the Maximal Invariant Statistic

This paper deals with the problem of adaptive multidimensional/multichannel signal detection in homogeneous Gaussian disturbance with unknown covariance matrix and structured deterministic interference. The aforementioned problem corresponds to a generalization of the well-known Generalized Multivariate Analysis of Variance (GMANOVA). In this first part of the work, we formulate the considered problem in canonical form and, after identifying a desirable group of transformations for the considered hypothesis testing, we derive a Maximal Invariant Statistic (MIS) for the problem at hand. Further…

Adaptive testing method for ergodic diffusion processes based on high frequency data

We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the adaptive estimator and provide three types of test statistics: likelihood ratio type test, Wald type test and Rao's score type test. It is proved that these test statistics converge in distribution to the chi-squared distribution under null hypothesis and have consistency of the tests against alternatives. Moreover, these test statistics converge in distribut…