GARCH (1,1) models are widely used for modelling processes with time varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a logtransform-based least squares estimator (LSE) for the GARCH (1,1) model. The asymptotic properties of the LSE are studied under very mild moment conditions for the errors. We establish the consistency...

AMS 2010 subject classifications: primary 62F12 62M05 secondary 60G52 60J75 Keywords: Asymptotic distribution of LSE Consistency of LSE Discrete observations Least squares method Stochastic processes Parameter estimation Small Lévy noises a b s t r a c t We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impo...

Land surface temperature (LST) is a key parameter for a wide number of applications, including hydrology, meteorology and surface energy balance. In this study, we first proposed a new land surface emissivity (LSE) scheme, including a lookup table-based method to determine the vegetated surface emissivity and an empirical method to derive the bare soil emissivity from the Global LAnd Surface Sa...

Imbalance band market is an alternative to traditional structures which proposed ensure that system frequency remains within acceptable bounds. In imbalance environment, the load-serving entities (LSEs) can purchase bands or reduce load deviation by operating a battery energy storage (BESS) avoid penalty for causing imbalance. The concept would be effective in sharing balancing responsibility b...

The null space method is a standard method for solving the linear least squares problem subject to equality constraints (the LSE problem). We show that three variants of the method, including one used in LAPACK that is based on the generalized QR factorization, are numerically stable. We derive two perturbation bounds for the LSE problem: one of standard form that is not attainable, and a bound...

This paper proposes the nonlinear Least Square Error (LSE) precoders for multiuser MIMO broadcast channels. The output signals of LSE Precoders are limited to be chosen from a predefined set which let these precoders address several constraints such as peak power limitation, constant envelope transmission and discrete constellations. We study the large-system performance of these precoders via ...

For spectrally efficient transmission over time-varying channels, the use of Adaptive Coding and Modulation (AMC) in wireless OFDM systems requires the estimation of radio channel at the receiver. This paper focuses on the use of time domain channel statistics, mainly concentrating on two schemes: Linear Minimum Mean Square Estimation (LMMSE) and Least Square Estimation (LSE) and their variants...

The aim of this study was to observe the relationship between dose-volume histogram (DVH) parameters and rectal late side effects (LSE) in computed tomography (CT)-based brachytherapy (BT) for patients with locally advanced cervical cancer. In total, 144 cervical cancer patients received external beam radiotherapy and CT-based BT. The data from 111 survival cases with pelvic local control (LC) ...

In this paper, we consider saliency detection problems from a unique perspective. We provide an implicit representation for the saliency map using level set evolution (LSE), and then combine LSE approach with energy functional minimization (EFM). Instead of introducing sophisticated segmentation procedures, we propose a flexible and lightweight LSE-EFM framework for saliency detection. The expe...

Time series linear regression model with the stationary residuals has been studied in many fields, and well established. However, the stationary assumption on the residuals seems to be restrictive. Therefore, we extend the model to the case when the residuals are locally stationary. The best linear unbiased estimator (BLUE) of coefficient vector contains the residual covariance matrix which is ...