Toshinari Kamakura

A consistent method of estimation for the three-parameter Weibull distribution

In this paper, we propose a new method for the estimation of parameters of the three-parameter Weibull distribution. The method is based on a data transformation, which avoids the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely in the entire parameter space, and the estimators also have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs better than some existing methods in terms of bias and root mean squared error (RMSE). Finally, two examples based on real data sets are presented to illustrate the proposed method.

Parameter Estimation of the Shape Parameter of the Castillo–Hadi Model

Abstract In Castillo and Hadi [Castillo, E., Hadi, A. S. (1995). Modeling lifetime data with application to fatigue models. J. Amer. Statist. Assoc. 90:1041–1054], a new model for the analysis of lifetime data in the presence of a covariate is presented. The model is derived based on physical and statistical considerations. In this article, we focus on estimation of the power parameter of this model, and propose the new methods for estimation based on the location-scale-free transformation.

The maximum full and partial likelihood estimators in the proportional hazard model

SummaryThe maximum full likelihood estimator in the proportional hazard model is explored in relation to the maximum partial likelihood estimator. In the scalar parameter case both the estimators have a common sign, and the absolute value of the former is strictly greater than that of the latter except for trivial cases. We point out also that the maximum full likelihood estimator after a simple modification of the likelihood equation provides a good approximation to the maximum partial likelihood estimator. Similar results are valid for the likelihood ratio tests.

A Consistent Method of Estimation For The Three-Parameter Gamma Distribution

For the three-parameter gamma distribution, it is known that the method of moments as well as the maximum likelihood method have difficulties such as non-existence in some range of the parameters, convergence problems, and large variability. For this reason, in this article, we propose a method of estimation based on a transformation involving order statistics from the sample. In this method, the estimates always exist uniquely over the entire parameter space, and the estimators also have consistency over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties.

Human detection algorithm for Doppler radar using prediction error in autoregressive model

Using a Doppler radar as a motion sensor is promising for monitoring human daily activities. Various detection algorithms for human activities and vital signs have been proposed; however, most require a controlled environment and do not allow for the presence of moving objects in the sensing area. In actuality, motor-actuated appliances such as electric fans and heaters are often noise sources in homes. The velocities of such appliances overlap with those of a person and can cause a Doppler effect even without human presence. We resolve this issue in the current study by analyzing motion regularity. To detect the irregular motions that characterize a persons presence, we utilize the prediction errors from an autoregressive model. A performance evaluation of the proposed algorithm shows that high accuracy is achieved for human detection under disturbances caused by electric appliance motions. Moreover, our method outperforms the conventional frequency-based method that uses power spectra of the Doppler signal.

On the Use of Particle Filters for Bayesian Image Restoration

Image restoration is one of the wide variety of branches in image analysis. In recent work, the Bayesian approach to the restoration has attracted interest and much of this work involves the use of statistical modeling for images assuming Markov random fields (MRF), the stochastic technique based on Monte Carlo methods and maximum a posteriori (MAP) estimation.

Indoor location estimation based on the RSS method using radial log-normal distribution

We study the problem of analyzing indoor location estimation by statistical radial distribution model. In this study, we suppose the observed distance data between transmitter and receiver as a radial log-normal distribution. We estimate the subjects location using marginal likelihoods of radial lognormal distribution. To demonstrate the effectiveness of our method, we conducted two sets of experiments, assessing the accuracy of location estimation of static case and dynamic case. In static experiment, subject is stationary state in some places in the chamber. This experiment is able to measure the precise performance of proposed method. In dynamic experiment, subject is move around in the chamber. This experiment is able to measure the suitability for practical use of proposed method. As a result, our method shows high accuracy for the static case indoor spatial location estimation.

Human Gait Modeling and Statistical Registration for the Frontal View Gait Data with Application to the Normal/Abnormal Gait Analysis

We study the problem of analyzing and classifying frontal view human gait data by registration and modeling on a video data. In this study, we suppose that frontal view gait data as a mixing of scale changing, human movements and speed changing parameter. Our gait model is based on human gait structure and temporal-spatial relations between camera and subject. To demonstrate the effectiveness of our method, we conducted two sets of experiments, assessing the proposed method in gait analysis for young/elderly person and abnormal gait detecting. In abnormal gait detecting experiment, we apply K-NN classifier, using the estimated parameters, to perform normal/abnormal gait detect, and present results from an experiment involving 120 subjects (young person), and 60 subjects (elderly person). As a result, our method shows high detection rate.

TREND ANALYSIS OF MULTIPLE COUNTING PROCESSES

We deal with the problem of the inference on the trend parameter that is common to multiple independent processes with different base-line intensities assuming nonhomogeneous Poisson processes. Two parametric intensity models are well investigated with focus on bias reduction and conditional inference. We present the theorem for conditional inference on the trend parameter.

A Simulation Study on Indoor Location Estimation Based on the Extreme Radial Weibull Distribution

In this study, we investigate the possibility of analyzing indoor location estimation under the NLoS environment by radial extreme value distribution model based on the simulation. We assume that the observed distance between the transmitter and receiver is a statistical radial extreme value distribution. The proposed method is based on the marginal likelihoods of radial extreme value distribution generated by positive distribution among several transmitter radio sites placed in a room. Okusa and Kamakura (Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2017) [16] not discussed the more detail performance of radial distribution based approach. To cope with this, to demonstrate the effectiveness of the proposed method, we carried out a simulation experiments. Results indicate that high accuracy was achieved when the method was implemented for indoor spatial location estimation.