Nonparametric Statistics: 4th ISNPS, Salerno, Italy, June 2018

Preface
Contents
Portfolio Optimisation via Graphical Least Squares Estimation
1 Introduction
2 Graph Theory and Matrices
2.1 Graph Theory
2.2 Matrices
3 The Idea of GLSE
4 Model Selection
5 Simulation Study
6 Data Analysis
7 Conclusion
References
Change of Measure Applications in Nonparametric Statistics
1 Introduction
2 Smooth Models
2.1 The Two-Sample Ranking Problem
2.2 The Use of Penalized Likelihood
3 Bayesian Models for Ranking Data
3.1 Maximum Likelihood Estimation (MLE) of Our Model
3.2 One-Sample Bayesian Method with Conjugate Prior
3.3 Two-Sample Bayesian Method with Conjugate Prior
4 Conclusion
References
Choosing Between Weekly and Monthly Volatility Drivers Within a Double Asymmetric GARCH-MIDAS Model
1 Introduction
2 Modelling Volatility with the DAGM Model
2.1 The DAGM Framework
2.2 The Role of VIX in the S&P 500 Volatility Dynamics
3 Wrapping Up
References
Goodness-of-fit Test for the Baseline Hazard Rate
1 Introduction
2 Estimation
3 Goodness-of-Fit Test
References
Permutation Tests for Multivariate Stratified Data: Synchronized or Unsynchronized Permutations?
1 Introduction
2 An Algorithm for NPC-based Stratified Tests
3 Synchronized and Unsynchronized Permutations
4 An Example Application
References
An Extension of the DgLARS Method to High-Dimensional Relative Risk Regression Models
1 Introduction
2 Relative Risk Regression Models
3 DgLARS Method for Relative Risk Regression Models
3.1 Differential Geometrical Structure of a Relative Risk Regression Model
3.2 The Extension of the DgLARS Method
4 Simulation Studies: Comparison with Other Variable Selection Methods
5 Finding Genetic Signatures in Cancer Survival
6 Conclusions
References
A Kernel Goodness-of-fit Test for Maximum Likelihood Density Estimates of Normal Mixtures
1 Introduction
2 Setup and Notation
3 Distribution of n Under the Null
4 An Example
5 Proof of Theorem 1
References
Robust Estimation of Sparse Signal with Unknown Sparsity Cluster Value
1 Introduction
2 Setting and Notation
3 Empirical Bayes Approach
3.1 Multivariate Normal Prior
3.2 Empirical Bayes Posterior
4 Known Sparsity Cluster Value: Thresholding Procedures
5 EBMA and EBMS Procedures for the Case of Unknown Sparsity Cluster Value
6 Comparative Simulation Study
References
Test for Sign Effect in Intertemporal Choice Experiments: A Nonparametric Solution
1 Introduction
2 Intertemporal Choice and Sign Effect
3 A Sample Survey
4 Multivariate Multistrata Test for Sign Effect
5 Nonparametric Solution
6 Case Study
7 Conclusions
References
Nonparametric First-Order Analysis of Spatial and Spatio-Temporal Point Processes
1 Introduction
2 First-Order Intensity Estimation
3 Testing Problems
4 Real Data Analysis
References
Bayesian Nonparametric Prediction with Multi-sample Data
1 Introduction
2 Hierarchical Processes Based on Completely Random Measures
2.1 Hierarchical Normalized CRMs
2.2 Hierarchical Pitman–Yor Processes
3 Prediction in Species Models
3.1 Numerical Experiments
4 Discussion
References
Algorithm for Automatic Description of Historical Series of Forecast Error in Electrical Power Grid
1 Introduction
2 Algorithm
2.1 Preprocessing
2.2 Descriptive Statistics
2.3 Clustering Algorithms
3 Case Study
4 Conclusion
References
Linear Wavelet Estimation in Regression with Additive and Multiplicative Noise
1 Introduction
2 Basics on Wavelets and Besov Balls
3 Assumptions, Estimators, and Main Result
4 Simulation Study
5 Conclusion
6 Proofs
References
Speeding up Algebraic-Based Sampling via Permutations
1 Introduction
2 Markov Chain Monte Carlo Samplings
2.1 MCMC—Vector-Based
2.2 MCMC—Orbit-Based
3 Comparison of Vector-Based and Orbit-Based MCMC
4 Simulation Study
4.1 Convergence Comparison
4.2 Accuracy Comparison
5 Conclusions
References
Obstacle Problems for Nonlocal Operators: A Brief Overview
1 Introduction
1.1 Representations of Lévy Processes
1.2 Connections to Integro-Differential Operators
1.3 Stochastic Integro-Differential Equations
1.4 Obstacle Problems
1.5 Review of Literature and Outline of the Survey
2 Motivating Examples
2.1 Variance Gamma Process
2.2 Regular Lévy Processes of Exponential Type
3 Statements of the Main Results
3.1 Stationary Obstacle Problem
3.2 Evolution Obstacle Problem
4 Concluding Remarks
References
Low and High Resonance Components Restoration in Multichannel Data
1 Introduction
2 Statistical Model
3 Estimation
4 Numerical Experiments
References
Kernel Circular Deconvolution Density Estimation
1 Introduction
2 Preliminaries
2.1 Trigonometric Moments and Fourier Series
2.2 Circular Density Estimation in the Error-Free Case
3 Kernel Density Estimator in the Errors-in-Variables Case
4 Simulations
5 Real Data Example
References
Asymptotic for Relative Frequency When Population Is Driven by Arbitrary Unknown Evolution
1 Introduction
2 Convergence Elements
3 A General SLLN via Permutations
4 Estimating E(Y(t))
5 Remarks
References
Semantic Keywords Clustering to Optimize Text Ads Campaigns
1 Introduction
2 Formalization of the Bidding Problem
3 The Word2Vec Modeling
3.1 The Behavioral Distance
3.2 The Model Training and the Semantic Distance
4 Keyword Clusterization
5 A/B Testing and Conclusions
References
A Note on Robust Estimation of the Extremal Index
1 Introductory Notes
2 Extremal Index Estimation
3 Introducing Robustness
3.1 Parametric Distribution of the Limiting Cluster Size
3.2 Robust Estimators
4 A Simulation Study
4.1 Simulation Study Design
5 Final Comments
References
Multivariate Permutation Tests for Ordered Categorical Data
1 Introduction
2 A Typical Medical Example
3 The Two-Sample Basic Problem
3.1 The 2timesK One-Dimensional Case
3.2 The 2timesK Multidimensional Case
4 The C-sample Stochastic Ordering Problem
5 Solution of Medical Example
6 Concluding Remarks
References
Smooth Nonparametric Survival Analysis
1 Introduction
2 Local Linear Estimation of the Distribution Function and Its Derivatives
3 Asymptotic Properties
4 Proofs and Auxiliary Lemmas
4.1 Proof of Theorem 1
References
Density Estimation Using Multiscale Local Polynomial Transforms
1 Introduction
2 The Multiscale Local Polynomial Transform (MLPT)
2.1 Local Polynomial Smoothing as Prediction
2.2 The Update Lifting Step
2.3 The MLPT Frame
2.4 The MLPT on Highly Irregular Grids
3 A Regression Model for Density Estimation
4 Sparse Variable Selection and Estimation in the Exponential Regression model
5 Fine-Tuning the Selection Threshold
6 Illustration and Concluding Discussion
References
On Sensitivity of Metalearning: An Illustrative Study for Robust Regression
1 Metalearning
2 Description of the Study
2.1 Primary Learning
2.2 Metalearning
3 Results
3.1 Primary Learning
3.2 Metalearning
4 Conclusions
References
Function-Parametric Empirical Processes, Projections and Unitary Operators
1 Basic Setup
2 Discrete Distributions
3 Uniform Empirical Process on [0,1]d
4 Parametric Hypotheses in mathbbRd
5 Distribution Free Testing for Linear Regression
References
Rank-Based Analysis of Multivariate Data in Factorial Designs and Its Implementation in R
1 Introduction
2 Large Sample Sizes nij
3 Small Sample Sizes nij, Large Number a of Samples
4 Conclusion
References
Tests for Independence Involving Spherical Data
1 Introduction
2 Testing Independence in the Bivariate Case
3 Computations and Extensions
3.1 Test on the Torus
3.2 Extension to Arbitrary Dimension
3.3 Consistency
4 Simulations
References
Interval-Wise Testing of Functional Data Defined on Two-dimensional Domains
1 Introduction
2 Previous Works: The IWT for Functional Data Defined on One-Dimensional Domains
3 Methods
3.1 The Extension of the IWT to Functional Data Defined on Two-Dimensional Domains
3.2 The Problem of Dimensionality in the Choice of the Neighbourhood
4 Simulation Study
4.1 Simulation Settings
4.2 Results of Simulation Study
5 Discussion
References
Assessing Data Support for the Simplifying Assumption in Bivariate Conditional Copulas
1 Introduction
2 Problem Setup
2.1 The Cross-Validated Pseudo Marginal Likelihood and Its Conditional Variant
2.2 Watanabe–Akaike Information Criterion
3 Detecting Data Support for SA
4 Simulations
4.1 Simulation Details
4.2 Simulation Results
5 Conclusion
References
Semiparametric Weighting Estimations of a Zero-Inflated Poisson Regression with Missing in Covariates
1 Preliminaries
2 Review of Zero-Inflated Model and Naive Estimation
3 Proposed Methods
3.1 Fully Kernel-Assisted Estimation
3.2 Fully GAMs-Assisted Estimation
3.3 Mixed Nuisance Functions-Assisted Estimation
4 Large Sample
5 Simulation Study
6 Discussion
References
The Discrepancy Method for Extremal Index Estimation
1 Introduction
2 Related Work
3 Main Results
3.1 Theory
3.2 Discrepancy Equation Based on the Chi-Squared Statistic
3.3 Estimation of k
4 Simulation Study
4.1 Models
4.2 Estimators and Their Comparison
5 Conclusions
References
Correction for Optimisation Bias in Structured Sparse High-Dimensional Variable Selection
1 Introduction
2 The Mirror Effect
3 Qualitative Description of the Mirror
3.1 Unstructured Signal-Plus-Noise Models
3.2 Structured Models: Grouped Variables
4 Simulation
5 Conclusion
References
United Statistical Algorithms and Data Science: An Introduction to the Principles
1 The Gorilla in the Room
2 The Design Principle
2.1 From Principles to Construction
3 Universality Properties
4 The Age of Unified Algorithms Is Here
5 The Three Pillars
References
The Halfspace Depth Characterization Problem
1 Introduction: Depth and Characterization of Measures
2 Negative Results
2.1 Counter-Example for Probability Measures
2.2 Counter-Example for Finite Measures
3 Comments on Some Positive Results
3.1 Sufficient Conditions for Discrete Distributions
3.2 Sufficient Conditions for Absolutely Continuous Distributions
4 Characterization Problem: Summary
References
A Component Multiplicative Error Model for Realized Volatility Measures
1 Introduction
2 Model Specification
3 Estimation
4 Empirical Application
5 Concluding Remarks
References
Asymptotically Distribution-Free Goodness-of-Fit Tests for Testing Independence in Contingency Tables of Large Dimensions
1 Introduction
2 Preliminaries
3 Method
4 Simulation
References
Incorporating Model Uncertainty in the Construction of Bootstrap Prediction Intervals for Functional Time Series
1 Introduction
2 Bootstrapping Prediction Intervals
2.1 The Bootstrap Method
3 Numerical Studies
References
Measuring and Estimating Overlap of Distributions: A Comparison of Approaches from Various Disciplines
1 Introduction
2 Methodology
2.1 Estimator of the OVL
2.2 Overlap of Private Datasets Using Cryptosets
2.3 Overlap Volume in a Probabilistic Interpretation
3 Data Examples and Comparison
References
Bootstrap Confidence Intervals for Sequences of Missing Values in Multivariate Time Series
1 Introduction
2 The Model and the Iterative Imputation Procedure
3 Bootstrap Confidence Intervals for Missing Values
4 A Monte Carlo Simulation Study
5 Concluding Remarks
References
On Parametric Estimation of Distribution Tails
1 Introduction
2 Main Results
3 Simulation Study
References
An Empirical Comparison of Global and Local Functional Depths
1 Introduction
2 Comparing Global and Local Depths: Real Data Examples
2.1 Phonemes Data
2.2 Nitrogen Oxides (NOx) Data
3 Comparing Global and Local Depths: FSD Versus KFSD
4 Simulation Study
5 Conclusions
References
AutoSpec: Detecting Exiguous Frequency Changes in Time Series
1 Introduction
2 Model and Existing Methods
2.1 AdaptSpec
2.2 AutoParm
2.3 The Problem Is Resolution
3 AutoSpec—Parametric
4 AutoSpecNP—Nonparametric
5 Spectral Resolution and a Simulation
References
Bayesian Quantile Regression in Differential Equation Models
1 Introduction
2 Methodology and Computation
3 Simulation Study
4 Realdata Analysis
References
Predicting Plant Threat Based on Herbarium Data: Application to French Data
1 Data Description
1.1 Herbarium
1.2 TPL and International Databases
1.3 IUCN Redlist
2 Methods
2.1 Text Mining
2.2 Dealing with Synonyms
2.3 Construction of the Predictors
2.4 Random Uniform Forests
3 Main Results
4 Perspectives
References
Monte Carlo Permutation Tests for Assessing Spatial Dependence at Different Scales
1 Introduction
2 Assessing Spatial Dependence at Different Scales
2.1 Permutation Test for Overall Spatial Dependence
2.2 Modified Permutation Test for Overall Spatial Dependence
2.3 Permutation Test for Spatial Dependence at Small Scales
3 Simulation Study
3.1 Simulation Setup
3.2 Simulation Results
4 Discussion and Outlook
References
Introduction to Independent Counterfactuals
1 Introduction
2 Framework
2.1 Estimation
3 Interpretation
3.1 Exogenous Linear Model
3.2 Endogenous Linear Model
4 Illustration
5 Conclusions
References
The Potential for Nonparametric Joint Latent Class Modeling of Longitudinal and Time-to-Event Data
1 Introduction
2 The JLCM Setup
3 Latent Class Membership of JLCM
4 Running Time of JLCM
5 Limitation to Time-Invariant Covariates
6 Nonparametric Approach for Joint Modeling
References
To Rank or to Permute When Comparing an Ordinal Outcome Between Two Groups While Adjusting for a Covariate?
1 Introduction
2 The Nonparametric Combination Method and a Pseudo-rank-based Approach
2.1 The Nonparametric Combination Method, Applied to an Anderson–Darling type Permutation Test
2.2 A Nonparametric (Pseudo-)Rank-based Method for Factorial Designs
3 Simulations
4 Real-Life Data Example
5 Discussion
References