scholarly journals Integral Least-Squares Inferences for Semiparametric Models with Functional Data

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Limian Zhao ◽  
Peixin Zhao
Keyword(s):  
Data Analysis ◽  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Functional Data ◽  
Estimation Method ◽  
Real Data ◽  
Semiparametric Models ◽  
Simulation Studies ◽  
Finite Sample

The inferences for semiparametric models with functional data are investigated. We propose an integral least-squares technique for estimating the parametric components, and the asymptotic normality of the resulting integral least-squares estimator is studied. For the nonparametric components, a local integral least-squares estimation method is proposed, and the asymptotic normality of the resulting estimator is also established. Based on these results, the confidence intervals for the parametric component and the nonparametric component are constructed. At last, some simulation studies and a real data analysis are undertaken to assess the finite sample performance of the proposed estimation method.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications

1993 ◽  
Vol 9 (2) ◽  
pp. 263-282 ◽  
Author(s):  
In Choi
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Unit Roots ◽  
Small Sample ◽  
Asymptotic Distributions ◽  
Standard Normal Distribution ◽  
Finite Sample ◽  
Standard Normal ◽  
Least Squares Estimates

Using the asymptotic normality of the least-squares estimates for the autoregressive (AR) process with real, positive unit roots and at least one stable root, we consider the asymptotic distributions of the Wald and t ratio tests on AR coefficients. In addition, we propose a method of constructing confidence intervals for the sum of AR coefficients possibly in the presence of a unit root. Using simulation methods, we compare the finite-sample cumulative distributions of the t ratios for individual autoregressive coefficients with those of standard normal distributions, and investigate the finite-sample performance of our confidence intervals and t ratios. Our simulation results show that the t ratios for nonstationary processes converge to a standard normal distribution more slowly than those for stationary processes. Further, the confidence intervals are shown to work reasonably well in moderately large samples, but they display unsatisfactory performance at small sample sizes.

scholarly journals Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

2021 ◽  
Author(s):  
Shuhei Ota ◽  
Mitsuhiro Kimura
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Algorithm ◽  
Simulation Studies

AbstractThis paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ($$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ 2 d - d - 1 dependence parameters to be estimated; therefore, maximum likelihood estimation is not practical for a large d from the viewpoint of computational complexity. Besides, the restriction for the FGM copula’s parameters becomes increasingly complex as d becomes large, which makes parameter estimation difficult. We propose an effective estimation algorithm for the d-variate FGM copula by using the method of inference functions for margins under the restriction of the parameters. We then discuss its asymptotic normality as well as its performance determined through simulation studies. The proposed method is also applied to real data analysis of bearing reliability.

scholarly journals Detection of Anomalies in Water Networks by Functional Data Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Laura Millán-Roures ◽  
Irene Epifanio ◽  
Vicente Martínez
Keyword(s):  
Data Analysis ◽  
Outlier Detection ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Water Networks ◽  
Archetypal Analysis ◽  
Detection Techniques ◽  
Second Stage ◽  
Two Phases

A functional data analysis (FDA) based methodology for detecting anomalous flows in urban water networks is introduced. Primary hydraulic variables are recorded in real-time by telecontrol systems, so they are functional data (FD). In the first stage, the data are validated (false data are detected) and reconstructed, since there could be not only false data, but also missing and noisy data. FDA tools are used such as tolerance bands for FD and smoothing for dense and sparse FD. In the second stage, functional outlier detection tools are used in two phases. In Phase I, the data are cleared of anomalies to ensure that data are representative of the in-control system. The objective of Phase II is system monitoring. A new functional outlier detection method is also proposed based on archetypal analysis. The methodology is applied and illustrated with real data. A simulated study is also carried out to assess the performance of the outlier detection techniques, including our proposal. The results are very promising.

scholarly journals A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2083
Author(s):  
Won-Tak Hong ◽  
Jiwon Lee ◽  
Eunju Hwang
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Average Length ◽  
Real Data ◽  
Spot Price ◽  
Correlated Errors ◽  
Sample Mean ◽  
Q Model ◽  
Multiple Assets ◽  
Least Squares Estimates

In this work, multivariate heterogeneous autoregressive-realized volatility (HAR-RV) models are discussed with their least squares estimations. We consider multivariate HAR models of order p with q multiple assets to explore the relationships between two or more assets’ volatility. The strictly stationary solution of the HAR(p,q) model is investigated as well as the asymptotic normality theories of the least squares estimates are established in the cases of i.i.d. and correlated errors. In addition, an exponentially weighted multivariate HAR model with a common decay rate on the coefficients is discussed together with the common rate estimation. A Monte Carlo simulation is conducted to validate the estimations: sample mean and standard error of the estimates as well as empirical coverage and average length of confidence intervals are calculated. Lastly, real data of volatility of Gold spot price and S&P index are applied to the model and it is shown that the bivariate HAR model fitted by selected optimal lags and estimated coefficients is well matched with the volatility of the financial data.

scholarly journals Resampling methods for functional data

2018 ◽  
Author(s):  
Timothy McMurry ◽  
Dimitris Politis
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Nonparametric Regression ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Confidence Bands ◽  
Resampling Methods ◽  
Current State ◽  
Inference Techniques

This article examines the current state of methodological and practical developments for resampling inference techniques in functional data analysis, paying special attention to situations where either the data and/or the parameters being estimated take values in a space of functions. It first provides the basic background and notation before discussing bootstrap results from nonparametric smoothing, taking into account confidence bands in density estimation as well as confidence bands in nonparametric regression and autoregression. It then considers the major results in subsampling and what is known about bootstraps, along with a few recent real-data applications of bootstrapping with functional data. Finally, it highlights possible directions for further research and exploration.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

2020 ◽  
Vol 45 (6) ◽  
pp. 719-749
Author(s):  
Eduardo Doval ◽  
Pedro Delicado
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Simulated Data ◽  
Real Data ◽  
Response Patterns ◽  
Fit Indices ◽  
Person Fit ◽  
Data Set ◽  
Aberrant Response Patterns

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

scholarly journals DGQR estimation for interval censored quantile regression with varying-coefficient models

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0240046
Author(s):  
ChunJing Li ◽  
Yun Li ◽  
Xue Ding ◽  
XiaoGang Dong
Keyword(s):  
Quantile Regression ◽  
Estimation Method ◽  
Real Data ◽  
Regression Estimation ◽  
Varying Coefficient Models ◽  
Simulation Studies ◽  
Varying Coefficient ◽  
Censored Quantile Regression ◽  
Direct Generalization ◽  
Interval Censored

This paper propose a direct generalization quantile regression estimation method (DGQR estimation) for quantile regression with varying-coefficient models with interval censored data, which is a direct generalization for complete observed data. The consistency and asymptotic normality properties of the estimators are obtained. The proposed method has the advantage that does not require the censoring vectors to be identically distributed. The effectiveness of the method is verified by some simulation studies and a real data example.

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