Two-step Maximum Likelihood Method Research Articles

A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan

In this study, a new horizontal ground-motion model is developed for crustal and subduction earthquakes in Taiwan. A novel two-step maximum-likelihood method is used as a regression tool to develop this model. This method simultaneously considers both the correlation between records and the biased sampling because of random truncation. Moreover, additional ground-motion data can be considered to derive more reliable analysis results. The functional form of the proposed ground-motion model is constructed using the response spectrum of the reference ground-motion scenario and different scalings of the source, path, and site to illustrate the ground-motion characteristics. The variabilities in the ground-motion intensity that result from different events, stations, and records are developed individually to derive a single-station sigma. The proposed ground-motion model may be useful for predicting ground-motion intensity and performing site-specific probabilistic seismic hazard analysis in Taiwan.

A Novel Regression Analysis Method for Randomly Truncated Strong-Motion Data

Regression analysis is a basic and essential tool for developing the ground motion prediction equation (GMPE). Generally, the probability of intensity measurement for a given ground motion scenario described by several predictors is assumed to be normally distributed. However, because of the triggering threshold of the strong-motion station, ground motion records below the triggering threshold are truncated (i.e., not recorded), and the truncated intensity levels of spectral accelerations at different periods are random variables. Consequently, the sampling of the ground motion data used in GMPE development is biased, and the observed probability of the intensity measurement is no longer normally distributed. Therefore, a novel two-step maximum-likelihood method is proposed in this paper as a regression tool to overcome this problem in GMPE development. The advantage of the proposed method is that the correlation between records from the same events and those from the same sites as well as the biased sampling problem can be considered simultaneously, and more ground motion data can be considered to derive more reliable analysis results.

APPLYING A TWO-STEP MAXIMUM LIKELIHOOD METHOD TO EXAMINE THE DEPOSIT INSURANCE PROGRAM OF TAIWAN

This paper examines the deposit insurance program of Taiwan. We adopt Duan et al. [4]'s deposit insurance pricing model, and estimate the deposit insurance premium by the Duan and Simonato two-step maximum likelihood method [5]. Our results show that the maximum likelihood estimates for the deposit insurance premium are considerably higher than the official rates currently charged by the Central Deposit Insurance Corporation (CDIC), the deposit insuring agency of Taiwan, indicating that the CDIC deposit insurance program appears to hand out a substantial subsidy to the banks in Taiwan. Our results also show that the CDIC in fact grants too much capital forbearance to the banks, and that the semiannual bank audits currently mandated by the CDIC are in fact much less frequent than our estimated values. These findings may also explain why the estimated rates for the deposit insurance premium are much higher than the current CDIC rates.

Dependence structures in Chinese and US financial markets: a time-varying conditional copula approach

In this article, we use a time-varying conditional copula approach to model Chinese and US stock markets’ dependence structures with other financial markets. The Autoregressive-Generalized Autoregressive Conditional Heteroscedastic-t (AR-GARCH-t) model is used to examine the marginal distributions, while Normal and Generalized Joe-Clayton (GJC) copula models are employed to analyse the joint distributions. In this pairwise analysis, both constant and time-varying conditional dependence parameters are estimated by a two-step maximum likelihood method. A comparative analysis of dependence structures in Chinese versus US stock markets is also provided. There are three main findings: first, the time-varying-dependence model does not always perform better than constant-dependence model. This result has not previously been reported in the literature. Second, we find that the upper tail dependence is much higher than the lower tail dependence in some short periods, which has not been documented in previous liter...

Dependence Structures in Chinese and U.S. Financial Markets: A Time-Varying Conditional Copula Approach

In this paper, we use a Time-Varying Conditional Copula approach (TVCC) to model Chinese and U.S. stock markets, dependence structures with other financial markets. The AR-GARCH-t model is used to examine the marginals, while Normal and Generalized Joe-Clayton copula models are employed to analyze the joint distributions. In this pairwise analysis, both constant and time-varying conditional dependence parameters are estimated by a two-step maximum likelihood method. A comparative analysis of dependence structures in Chinese versus U.S. stock markets is also provided. There are three main findings: First, the time-varying-dependence model does not always perform better than constant-dependence model. This result has not previously been reported in the literature. Second, although previous research extensively reports that the lower tail dependence between stock markets tends to be higher than the upper tail dependence, we find a counterexample where the upper tail dependence is much higher than the lower tail dependence in some short periods. Last, Chinese financial market is relatively separate from other international financial markets in contrast to the U.S. market. The tail dependence with other financial markets is much lower in China than in the U.S.

Automobile Insurance Contracts and Risk of Accident: An Empirical Test Using French Individual Data

Insurance has for a long time been perceived as a way of transferring responsibility from insured agents to insurers and thus as potentially influencing insured agents' behavior. Two particular opportunistic behaviors have been analyzed. First, the theory of adverse selection predicts that high-risk agents are likely to demand more insurance than are low-risk agents. Second, the theory of moral hazard predicts that the wider the insurance coverage, the less agents will try to prevent accidents. Both theories thus conclude that agents who are totally insured should have a higher probability of accident than those with only partial insurance, ceteris paribus. Nevertheless, one of the aims of insurance rating systems is to control for these opportunistic behaviors. In this article, we use individual data to see if the French automobile insurance rating system has achieved this aim. We do this using a two-step maximum-likelihood method. First, we compute a probit model to estimate the probability of taking out comprehensive versus third-party insurance. We then calculate the generalized residual, which is included as an independent variable in a negative binomial model estimating the probability of having an accident. The coefficient of this variable is argued to represent adverse selection and ex-ante moral-hazard behavior.

New TSML Algorithms for Multichannel Blind Identification

In this paper we present new two-step maximum likelihood (TSML) algorithms for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The original TSML method was developed as a fast alternative to the direct maximum likelihood approach. The TSML method exploits a novel orthogonal complement (OC) matrix of the generalized Sylvester matrix. Despite its statistical high-SNR efficiency, the original implementation of the TSML method is still computationally expensive as it requires O ( N ) flops, where N is the sample size. The new TSML algorithms shown in this paper are faster implementations (of order O ( N )) or modifications of the original TSML algorithm which are based on the exploitation of displacement structure of the OC matrix and a non-redundant OC matrix.

Fast maximum likelihood for blind identification of multiple FIR channels

This paper develops a fast maximum likelihood method for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the Cramer-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML, method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established.