The goal of regression analysis is to describe the stochastic relationship between a vector of inputs x and a scalar output y. This can be achieved by estimating the entire conditional density p(y|x). In this paper we present a new approach for nonparametric conditional density estimation. We develop a piecewise-linear path-following method for kernel-based quantile regression. It enables us to estimate the cumulative distribution function (CDF) of conditional density p(y|x) in piecewise-linear form. After smoothing the estimated piecewise-linear CDF, we obtain nonparametric conditional density estimatep(y|x) for all x in the input domain. Theoretical analyses and numerical experiments are presented for showing the effectiveness of the approach.

This paper proposes new force control strategies robust against disturbance and parameters variation. These strategies are expansions of disturbance observer which estimates disturbance and parameters variation of motors with simple computation. In this paper, we propose new observers estimate parameters variation of environment on which the force is imposed. Since the control system is fized to a nominal system b y the observers, second derivative of force can be controlled.We also propose a force control using controller of the second derivative of force. The force response similar to the force command is realized in spite of the disturbance and the parameters variation of the control object. The effectiveness is confirmed experimentally.

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We propose a new force control strategy which is robust against disturbance and parameters variation. This method U an expansion of disturbance observer which estimates disturbance and parameters variation of motors with simple computation. The new observer also estimates disturbance and parameters variation of environment on which the force is imposed. Since they are compensated by the new observer, similar force response to the force command is realized. The effectiveness of the proposed method is confirmed by some experimental results.

The goal of regression analysis is to describe the relationship between an output y and a vector of inputs x. Least squares regression provides how the mean of y changes with x, i.e. it estimates the conditional mean function. Estimating a set of conditional quantile functions provides a more complete view of the relationship between y and x. Quantile regression [1] is one of the promising approaches to estimate conditional quantile functions. Several types of quantile regression estimator have been studied in the literature. In this paper, we are particularly concerned with kernel-based nonparametric quantile regression formulated as a quadratic programing problem similar to those in support vector machine literature [2].A group of conditional quantile functions, say, at the orders q = 0.1, 0.2, . . . , 0.9, can provide a nonparametric description of the conditional probability density p(y|x). This requires us to solve many quadratic programming problems and it could be computationally demanding for large-scale problems. In this paper, inspired by the recently developed path following strategy [3][4], we derive an algorithm to solve a sequence of quadratic programming problems for the entire range of quantile orders q ∈ (0, 1). As well as the computational efficiency, the derived algorithm provides the full nonparametric description of the conditional distribution p(y|x). A few examples are given to illustrate the algorithm.