Comparing FPCA Based on Conditional Quantile Functions and FPCA Based on Conditional Mean Function

2019 ◽  
pp. 65-76
Author(s):  
M. Ruggieri ◽  
F. Di Salvo ◽  
A. Plaia
Keyword(s):  
Conditional Quantile ◽  
Conditional Mean ◽  
Quantile Functions ◽  
Mean Function

scholarly journals Quantile Regression

2001 ◽  
Vol 15 (4) ◽  
pp. 143-156 ◽  
Author(s):  
Roger Koenker ◽  
Kevin F Hallock
Keyword(s):  
Quantile Regression ◽  
Weighted Sum ◽  
Median Regression ◽  
Conditional Quantile ◽  
Conditional Mean ◽  
Regression Methods ◽  
Ceo Pay ◽  
Food Expenditure ◽  
Quantile Functions ◽  
Special Case

Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

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.

scholarly journals Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates

2019 ◽  
Vol 212 (2) ◽  
pp. 433-450 ◽  
Author(s):  
Xirong Chen ◽  
Degui Li ◽  
Qi Li ◽  
Zheng Li
Keyword(s):  
Nonparametric Estimation ◽  
Conditional Quantile ◽  
Quantile Functions

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

qmodel: A command for fitting parametric quantile models

2019 ◽  
Vol 19 (2) ◽  
pp. 261-293 ◽  
Author(s):  
Matteo Bottai ◽  
Nicola Orsini
Keyword(s):  
Quantile Regression ◽  
Simulated Data ◽  
Quantile Function ◽  
Parametric Models ◽  
Outcome Variable ◽  
Simple Type ◽  
Conditional Quantile ◽  
Quantile Functions ◽  
Conditional Quantile Function ◽  
Insight Into

In this article, we introduce the qmodel command, which fits parametric models for the conditional quantile function of an outcome variable given covariates. Ordinary quantile regression, implemented in the qreg command, is a popular, simple type of parametric quantile model. It is widely used but known to yield erratic estimates that often lead to uncertain inferences. Parametric quantile models overcome these limitations and extend modeling of conditional quantile functions beyond ordinary quantile regression. These models are flexible and efficient. qmodel can estimate virtually any possible linear or nonlinear parametric model because it allows the user to specify any combination of qmodel-specific built-in functions, standard mathematical and statistical functions, and substitutable expressions. We illustrate the potential of parametric quantile models and the use of the qmodel command and its postestimation commands through realand simulated-data examples that commonly arise in epidemiological and pharmacological research. In addition, this article may give insight into the close connection that exists between quantile functions and the true mathematical laws that generate data.

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.

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
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