Characterization based on convex conditional mean function

2008 ◽  
Vol 138 (4) ◽  
pp. 964-970 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S.N.U.A. Kirmani
Keyword(s):  
Conditional Mean ◽  
Mean Function

Estimation of nonstationary nonparametric regression model with multiplicative structure

2021 ◽  
Author(s):  
Likai Chen ◽  
Ekaterina Smetanina ◽  
Wei Biao Wu
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Risk Premium ◽  
Convergence Rates ◽  
Broad Class ◽  
Estimation Procedure ◽  
Small Samples ◽  
Nonparametric Regression Model ◽  
Conditional Mean ◽  
Mean Function

Abstract This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth, and estimating the shape of the monthly risk premium for S&P 500 Index data.

scholarly journals COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS

2020 ◽  
pp. 1-33
Author(s):  
Abdelhakim Aknouche ◽  
Christian Francq
Keyword(s):  
Time Series ◽  
Conditional Distribution ◽  
Stochastic Orders ◽  
Conditional Mean ◽  
Contraction Condition ◽  
Mixing Coefficients ◽  
The Mean ◽  
Quasi Maximum Likelihood ◽  
Geometric Decay ◽  
Mean Function

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

Local polynomial estimation of a conditional mean function with dependent truncated data

Test ◽  
2011 ◽  
Vol 20 (3) ◽  
pp. 653-677 ◽  
Author(s):  
Han-Ying Liang ◽  
Jacobo de Uña-Álvarez ◽  
María del Carmen Iglesias-Pérez
Keyword(s):  
Truncated Data ◽  
Conditional Mean ◽  
Local Polynomial ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

scholarly journals TESTING GENERALIZED REGRESSION MONOTONICITY

2018 ◽  
Vol 35 (6) ◽  
pp. 1146-1200 ◽  
Author(s):  
Yu-Chin Hsu ◽  
Chu-An Liu ◽  
Xiaoxia Shi
Keyword(s):  
Instrumental Variable ◽  
Interval Data ◽  
Local Alternatives ◽  
Stochastic Monotonicity ◽  
Conditional Mean ◽  
Special Cases ◽  
Generalized Regression ◽  
Latent Structures ◽  
Image Position ◽  
Mean Function

We propose a test for a generalized regression monotonicity (GRM) hypothesis. The GRM hypothesis is the sharp testable implication of the monotonicity of certain latent structures, as we show in this article. Examples include the monotonicity of the conditional mean function when only interval data are available for the dependent variable and the monotone instrumental variable assumption of Manski and Pepper (2000). These instances of latent monotonicity can be tested using our test. Moreover, the GRM hypothesis includes regression monotonicity and stochastic monotonicity as special cases. Thus, our test also serves as an alternative to existing tests for those hypotheses. We show that our test controls the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives, and has nontrivial power against some ${n^{ - 1/2}}$ local alternatives.

scholarly journals New Insights Into Learning With Correntropy-Based Regression

2021 ◽  
Vol 33 (1) ◽  
pp. 157-173
Author(s):  
Yunlong Feng
Keyword(s):  
Minimum Distance ◽  
Convergence Rates ◽  
Distance Estimation ◽  
Information Theoretic Learning ◽  
Conditional Mean ◽  
Conditional Median ◽  
Conditional Mode ◽  
Big Picture ◽  
Regression Problems ◽  
Mean Function

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively studied and explored. Its application to regression problems leads to the robustness-enhanced regression paradigm: correntropy-based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy-based regression regresses toward the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in this study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm in fact provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, and the conditional median functions under certain conditions. Third, we present some new results when it is used to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional ([Formula: see text])-moment assumptions. The saturation effect on the established convergence rates, which was observed under ([Formula: see text])-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy-based regression, help cement the theoretic correntropy framework, and enable us to investigate learning schemes induced by general bounded nonconvex loss functions.

Regularized modal regression with data-dependent hypothesis spaces

2019 ◽  
Vol 17 (06) ◽  
pp. 1950047
Author(s):  
Yingjie Wang ◽  
Hong Chen ◽  
Biqin Song ◽  
Han Li
Keyword(s):  
Least Squares ◽  
Learning Community ◽  
Analysis Data ◽  
Learning Problems ◽  
Least Squares Regression ◽  
Conditional Mean ◽  
Learning Framework ◽  
Proposed Model ◽  
Modal Regression ◽  
Mean Function

Modal regression aims at learning the conditional mode function, which is different from the traditional least-squares for approximating the conditional mean function. Due to its robust to complex noise and outliers, modal regression has attracted increasing attention recently in statistics and machine learning community. However, most of the previous modal regression models are limited to learning framework with data-independent hypothesis spaces. Usually, the data-dependent hypothesis spaces can provide much flexibility and adaptivity for many learning problems. By employing data-dependent hypothesis spaces, we propose a new regularized modal regression and establish its generalization error analysis. Data experiments demonstrate the competitive performance of the proposed model over the related least-squares regression.

scholarly journals Weighted estimation of conditional mean function with truncated, censored and dependent data

Statistics ◽  
2018 ◽  
Vol 52 (6) ◽  
pp. 1249-1269 ◽  
Author(s):  
Han-Ying Liang ◽  
María del Carmen Iglesias-Pérez
Keyword(s):  
Dependent Data ◽  
Conditional Mean ◽  
Mean Function ◽  
Weighted Estimation
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