Uniform Consistency Research Articles

Tuning parameter-free nonparametric density estimation from tabulated summary data

Administrative data are often easier to access as tabulated summaries than in the original format due to confidentiality concerns. Motivated by this practical feature, we propose a novel nonparametric density estimation method from tabulated summary data based on maximum entropy and prove its strong uniform consistency. Unlike existing kernel-based estimators, our estimator is free from tuning parameters and admits a closed-form density that is convenient for post-estimation analysis. We apply the proposed method to the tabulated summary data of the U.S. tax returns to estimate the income distribution.

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

$U$-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. $U$-statistics generalise the empirical mean of a random variable $X$ to sums over every $m$-tuple of distinct observations of $X$. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional $U$-statistics. In the present work, we provide a new class of estimators of conditional $U$-statistics. More precisely, we investigate the conditional $U$-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over $\varphi \in \mathscr{F}$ for a suitably restricted class $\mathscr{F}$, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional $U$-statistics processes. We discuss the wild bootstrap of the conditional $U$-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.

FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series

We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by common factors, models the remaining idiosyncratic dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via l 1 -regularized Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarizes both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.

Estimation of large covariance matrices with mixed factor structures

Summary We extend the principal orthogonal complement thresholding (POET) framework by J. Fan, Y. Liao, and M. Mincheva (2013) to estimate large covariance matrices with a ‘mixed’ structure of observable and unobservable strong/weak factors, and we call this method the extended POET (ePOET). Especially, the weak factor structure allows the existence of slowly divergent eigenvalues of the covariance matrix that are frequently observed in real data. Under some mild conditions, we derive the uniform consistency of the proposed estimator for the cases with or without observable factors. Furthermore, several simulation studies show that the ePOET achieves good finite-sample performance regardless of data with strong, weak, or mixed factors structure. Finally, we conduct empirical studies to present the practical usefulness of the ePOET.

Techno-Economic Evaluation of a Strawberry Ice Cream Production Plant Proposal in Cuba

Ice cream is a solidified dairy product produced by freezing a pasteurized mixture by stirring to incorporate air and guarantee a uniform consistency. This product is in high demand among people of all ages. In the present work, we used the SuperPro Designer® tool to simulate an industrial-scale strawberry ice-cream production plant located in Cuba with an annual production capacity of approximately 830 ice-cream 10 L containers per batch (1 201 770 L per year). Through simulation, the mass and energy balances were determined, as well as the main economic and profitability indicators of the proposed production process. The unit production cost was USD $ 7.04/container, while the annual net profit was USD $ 980 000. The Net Present Value, Internal Rate of Return, and Payback period were USD $ 2 860 000, 24.29 %, and 3.94 years, respectively, which indicate that the proposed strawberry ice-cream production plant is feasible from the technical-economic point of view under the current economic conditions in Cuba.

Kernel methods for causal functions: dose, heterogeneous and incremental response curves

Abstract We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous and incremental response curves. The treatment and covariates may be discrete or continuous in general spaces. Because of a decomposition property specific to the reproducing kernel Hilbert space, our estimators have simple closed-form solutions. We prove uniform consistency with finite sample rates via an original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training programme for disadvantaged youths.

A PANEL CLUSTERING APPROACH TO ANALYZING BUBBLE BEHAVIOR

AbstractThis study provides new mechanisms for identifying and estimating explosive bubbles in mixed‐root panel autoregressions with a latent group structure. A postclustering approach is employed that combines k‐means clustering with right‐tailed panel‐data testing. Uniform consistency of the k‐means algorithm is established. Pivotal null limit distributions of the tests are introduced. A new method is proposed to consistently estimate the number of groups. Monte Carlo simulations show that the proposed methods perform well in finite samples; and empirical applications of the proposed methods identify bubbles in the U.S. and Chinese housing markets and the U.S. stock market.

Nonparametric estimation of the shape functions and related asymptotic results

Arriaza et al (Metrika 82:99–124, 2019) introduced the right and left shape functions, which enjoy interesting properties in terms of describing the global form of a distribution. This paper proposes and studies nonparametric estimators of those functions. The estimators involve nonparametric estimation of the quantile and density functions. Pointwise and uniform consistency are proved under general regularity assumptions, as well as the limit in law. Simulations are included to study the practical performance of the proposed estimators. The analysis of a real data set illustrates the methodology.

The analysis of semi‐competing risks data using Archimedean copula models

In this paper, we derive the copula‐graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi‐competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion.

Mean group instrumental variable estimation of time-varying large heterogeneous panels with endogenous regressors

The large heterogeneous panel data models are extended to the setting where the heterogenous coefficients are changing over time and the regressors are endogenous. Kernel-based non-parametric time-varying parameter instrumental variable mean group (TVP-IV-MG) estimator is proposed for the time-varying cross-sectional mean coefficients. The uniform consistency is shown and the pointwise asymptotic normality of the proposed estimator is derived. A data-driven bandwidth selection procedure is also proposed. The finite sample performance of the proposed estimator is investigated through a Monte Carlo study and an empirical application on multi-country Phillips curve with time-varying parameters.

On Uniform Consistency of Neyman’s Type Nonparametric Tests

On Uniform Consistency of Neyman’s Type Nonparametric Tests

TECHNOLOGY OF MINCED POULTRY PRODUCTS WITH INCREASED DIETARY FIBER CONTENT

The basis of the state policy of Ukraine in the field of healthy nutrition of the population for the period until 2025 is to preserve and strengthen the health of the population, prevention of diseases caused by poor and unbalanced nutrition. Food products enriched with irreplaceable components, including dietary fibers, have been developed. The article substantiates the use of broiler meat as the main ingredient of the recipe, selects and studies the vegetable supplement of oat bran, which contains dietary fibers. The functional-technological and organoleptic indicators of minced meat models with different amounts of vegetable additives were studied, as a result, the optimal dose of introduction was determined and the formulation of the product made from broiler meat with an increased content of dietary fibers was developed. Optimal modes of heat treatment of the semi-finished product using a steam convection oven and modes of cold treatment of the finished product in "shock" freezing chambers were selected. The thermophysical characteristics of the new product were studied, and the duration of its freezing was calculated using Planck's formula. The technology of production of a functional product from broiler meat is proposed. The developed product is characterized by high organoleptic characteristics, such as juiciness of the product, pleasant smell and taste, uniform consistency, as well as a large yield of the finished product. The product contains dietary fibers, in one portion their amount is 8 g, which contributes to the satisfaction of 40% of the body's daily need for this food substance. The optimal recipe and technology of chicken cutlets with dietary fibers have been scientifically substantiated and developed. The possibility of producing chicken cutlets with a high content of dietary fiber has been theoretically and experimentally substantiated. Based on the analysis of the chemical composition and the study of the content of dietary fibers, functional-technological and organoleptic indicators of six vegetable supplements, the feasibility of introducing the vegetable supplement "Oat bran" into the recipe of chicken cutlets was substantiated. The effectiveness of thermal processing of chicken cutlets with increased dietary fiber content when using a convection oven in the steam + convection mode compared to the traditional method of processing has been proven. The raw materials for the production of the finished product were selected, the recipe was developed, the heat treatment parameters were selected, and the technology of quick-frozen finished product was developed. The developed ready-made poultry dish has an increased nutritional value due to the content of dietary fibers. It is taken into account that dietary fibers should be a mandatory part of the diet. Their total content in one portion is 8 g per 125 g of the finished product, which meets the daily need for this indicator by 40%.

Expert Kaplan–Meier estimation

ABSTRACT The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the product-limit estimator in two different ways with distinct interpretations. Strong uniform consistency is proved for both cases under certain assumptions on the kind of contamination and the quality of expert information, which sheds light on the techniques and decisions that practitioners may take. The nuances of the techniques are discussed – also with a view towards semi-parametric estimation – and they are illustrated using simulated and real-world insurance data.

NUCLEAR NORM REGULARIZED QUANTILE REGRESSION WITH INTERACTIVE FIXED EFFECTS

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.

Rates of the Strong Uniform Consistency for the Kernel-Type Regression Function Estimators with General Kernels on Manifolds

Rates of the Strong Uniform Consistency for the Kernel-Type Regression Function Estimators with General Kernels on Manifolds

Uniform consistency in nonparametric mixture models

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The resulting analysis turns out to be nontrivial, and several novel technical tools are developed along the way. In the case of mixed regression, we prove L1 convergence of the regression functions while allowing for the component regression functions to intersect arbitrarily often, which presents additional technical challenges. We also consider generalizations to general (i.e., nonconvolutional) nonparametric mixtures.

Estimation of common factors for microstructure noise and efficient price in a high-frequency dual factor model

We develop the Double Principal Component Analysis (DPCA) based on a dual factor structure for high-frequency intraday returns contaminated with microstructure noise. The dual factor structure allows a factor structure for microstructure noise in addition to the factor structure for efficient log-prices. We construct estimators of factors for both efficient log-prices and microstructure noise as well as their common components, and provide uniform consistency of these estimators when the number of assets and the sampling frequency go to infinity. In a Monte Carlo exercise, we compare our DPCA method to a PCA-VECM method. Finally, an empirical analysis of intraday returns of S&P 500 Index constituents provides evidence of co-movement of the microstructure noise that distinguishes from latent systematic risk factors.

On uniform consistency of Neyman’s type nonparametric tests

The goodness-of-fit problem is explored, when the test statistic is a linear combination of squared Fourier coefficients’ estimates coming from the Fourier decomposition of a probability density. Common examples of such statistics include Neyman’s test statistics and test statistics, generated by L2-norms of kernel estimators. We prove the asymptotic normality of the test statistic for both the null and alternative hypothesis. Using these results we deduce conditions of uniform consistency for nonparametric sets of alternatives, which are defined in terms of distribution or density functions. Results on uniform consistency, related to the distribution functions, can be seen as a statement showing to what extent the distance method, based on a given test statistic, makes the hypothesis and alternatives distinguishable. In this case, the deduced conditions of uniform consistency are close to necessary. For sequences of alternatives - defined in terms of density functions - approaching the hypothesis in L2-metric, we find necessary and sufficient conditions for their consistency. This result is obtained in terms of the concept of maxisets, the description of which for given test statistics is found in this publication.

$ k $NN local linear estimation of the conditional density and mode for functional spatial high dimensional data

<abstract><p>Traditionally, regression problems are examined using univariate characteristics, including the scale function, marginal density, regression error, and regression function. When the correlation between the response and the predictor is reasonably straightforward, these qualities are helpful and instructive. Given the predictor, the response's conditional density provides more specific information regarding the relationship. This study aims to examine a nonparametric estimator of a scalar response variable's function of a density and mode, given a functional variable when the data are spatially dependent. The estimator is then derived and established by combining the local linear and the $ k $ nearest neighbors methods. Next, the suggested estimator's uniform consistency in the number of neighbors (UNN) is proved. Finally, to demonstrate the efficacy and superiority of the acquired results, we applied our new estimator to simulated and real data and compared it to the existing competing estimator.</p></abstract>

Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response

Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response