301 research outputs found
Estimation of multiple-regime regressions with least absolutes deviation
This paper considers least absolute deviations estimation of a regression model with multiple change points occurring at unknown times. Some asymptotic results, including rates of convergence and asymptotic distributions, for the estimated change points and the estimated regression coefficient are derived. Results are obtained without assuming that each regime spans a positive fraction of the sample size. In addition, the number of change points is allowed to grow as the sample size increases. Estimation of the number of change points is also considered. A feasible computational algorithm is developed. An application is also given, along with some monte carlo simulations.Multiple change points, multiple-regime regressions, least absolute deviation, asymptotic distribution
Least squares estimation of a shift in linear processes
This paper considers a mean shift with an unknown shift point in a linear process and estimates the unknown shift point (change point) by the method of least squares. Pre-shift and post-shift means are estimated concurrently with the change point. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained when the magnitude of shift is small. It is shown that serial correlation affects the variance of the change point estimator via the sum of the coefficients (impulses) of the linear process. When the underlying process is an ARMA, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimation.Mean shift; linear processes; change point; rate of convergence; order estimation; generalized residuals
Weak convergence of the sequential empirical processes of residuals in ARMA models
This paper studies the weak convergence of the sequential empirical process of the estimated residuals in ARMA(p,q) models when the errors are independent and identically distributed. It is shown that, under some mild conditions, converges weakly to a Kiefer process. The weak convergence is discussed for both finite and infinite variance time series models. An application to a change-point problem is considered.Time series models, residual analysis, sequential empirical process, weak convergence, Kiefer process, change-point problem
Structural changes, common stochastic trends and unit roots in panel data
In this paper we propose a new test statistic that considers multiple structural breaks to analyse the non-stationarity of a panel data set. The methodology is based on the common factor analysis in an attempt to allow for some sort of dependence across the individuals. Thus allowing for multiple structural breaks in the â€Panel Analysis of Non-stationarity in Idiosyncratic and Common components†(PANIC) methodology increases the degree of heterogeneity when assessing the stochastic properties of the panel data setmultiple structural breaks, common factors, panel data unit root tests, principal components
Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood
We study the estimation of a high dimensional approximate factor model in the
presence of both cross sectional dependence and heteroskedasticity. The
classical method of principal components analysis (PCA) does not efficiently
estimate the factor loadings or common factors because it essentially treats
the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated.
For efficient estimation it is essential to estimate a large error covariance
matrix. We assume the model to be conditionally sparse, and propose two
approaches to estimating the common factors and factor loadings; both are based
on maximizing a Gaussian quasi-likelihood and involve regularizing a large
covariance sparse matrix. In the first approach the factor loadings and the
error covariance are estimated separately while in the second approach they are
estimated jointly. Extensive asymptotic analysis has been carried out. In
particular, we develop the inferential theory for the two-step estimation.
Because the proposed approaches take into account the large error covariance
matrix, they produce more efficient estimators than the classical PCA methods
or methods based on a strict factor model
Statistical analysis of factor models of high dimension
This paper considers the maximum likelihood estimation of factor models of
high dimension, where the number of variables (N) is comparable with or even
greater than the number of observations (T). An inferential theory is
developed. We establish not only consistency but also the rate of convergence
and the limiting distributions. Five different sets of identification
conditions are considered. We show that the distributions of the MLE estimators
depend on the identification restrictions. Unlike the principal components
approach, the maximum likelihood estimator explicitly allows
heteroskedasticities, which are jointly estimated with other parameters.
Efficiency of MLE relative to the principal components method is also
considered.Comment: Published in at http://dx.doi.org/10.1214/11-AOS966 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Statistical Inferences Using Large Estimated Covariances for Panel Data and Factor Models
While most of the convergence results in the literature on high dimensional
covariance matrix are concerned about the accuracy of estimating the covariance
matrix (and precision matrix), relatively less is known about the effect of
estimating large covariances on statistical inferences. We study two important
models: factor analysis and panel data model with interactive effects, and
focus on the statistical inference and estimation efficiency of structural
parameters based on large covariance estimators. For efficient estimation, both
models call for a weighted principle components (WPC), which relies on a high
dimensional weight matrix. This paper derives an efficient and feasible WPC
using the covariance matrix estimator of Fan et al. (2013). However, we
demonstrate that existing results on large covariance estimation based on
absolute convergence are not suitable for statistical inferences of the
structural parameters. What is needed is some weighted consistency and the
associated rate of convergence, which are obtained in this paper. Finally, the
proposed method is applied to the US divorce rate data. We find that the
efficient WPC identifies the significant effects of divorce-law reforms on the
divorce rate, and it provides more accurate estimation and tighter confidence
intervals than existing methods
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