scholarly journals Estimating multi-index models with response-conditional least squares

2021 ◽  
Vol 15 (1) ◽  
pp. 589-629
Author(s):  
Timo Klock ◽  
Alessandro Lanteri ◽  
Stefano Vigogna
Keyword(s):  
Least Squares ◽  
Multi Index ◽  
Conditional Least Squares

scholarly journals On estimation of the variances for critical branching processes with immigration

2010 ◽  
Vol 47 (02) ◽  
pp. 526-542
Author(s):  
Chunhua Ma ◽  
Longmin Wang
Keyword(s):  
Least Squares ◽  
Branching Process ◽  
Branching Processes ◽  
Limiting Distributions ◽  
Least Squares Estimators ◽  
Conditional Least Squares ◽  
Regularly Varying ◽  
Branching Process With Immigration ◽  
Critical Branching Process

The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).

scholarly journals Asymptotic Optimality of Estimating Function Estimator for CHARN Model

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Tomoyuki Amano
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Financial Time Series ◽  
Asymptotic Optimality ◽  
Time Series Models ◽  
Estimating Function ◽  
Asymptotically Optimal ◽  
Financial Time ◽  
Conditional Least Squares ◽  
Better Than

CHARN model is a famous and important model in the finance, which includes many financial time series models and can be assumed as the return processes of assets. One of the most fundamental estimators for financial time series models is the conditional least squares (CL) estimator. However, recently, it was shown that the optimal estimating function estimator (G estimator) is better than CL estimator for some time series models in the sense of efficiency. In this paper, we examine efficiencies of CL and G estimators for CHARN model and derive the condition that G estimator is asymptotically optimal.

scholarly journals Fluctuation limit of branching processes with immigration and estimation of the means

2005 ◽  
Vol 37 (02) ◽  
pp. 523-538 ◽  
Author(s):  
M. Ispány ◽  
G. Pap ◽  
M. C. A. van Zuijlen
Keyword(s):  
Least Squares ◽  
Critical Case ◽  
Branching Processes ◽  
Critical Value ◽  
Subcritical Case ◽  
Asymptotically Normal ◽  
Fluctuation Limit ◽  
Conditional Least Squares ◽  
Type Process ◽  
Conditional Least Squares Estimator

We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n 3/2, in contrast to both the subcritical case, in which it is n 1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.

scholarly journals Asymptotic inference for nearly unstable INAR(1) models

2003 ◽  
Vol 40 (3) ◽  
pp. 750-765 ◽  
Author(s):  
M. Ispány ◽  
G. Pap ◽  
M. C. A. van Zuijlen
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Limiting Distribution ◽  
Least Squares Estimator ◽  
Asymptotic Inference ◽  
First Order ◽  
Conditional Least Squares ◽  
Conditional Least Squares Estimator

A sequence of first-order integer-valued autoregressive (INAR(1)) processes is investigated, where the autoregressive-type coefficient converges to 1. It is shown that the limiting distribution of the conditional least squares estimator for this coefficient is normal and the rate of convergence is n3/2. Nearly critical Galton–Watson processes with unobservable immigration are also discussed.

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