Data Mining in Automotive Warranty Analysis

<p>This thesis is about data mining in automotive warranty analysis, with an emphasis on modeling the mean cumulative warranty cost or number of claims (per vehicle). In our study, we deal with a type of truncation that is typical for automotive warranty data, where the warranty coverage and the resulting warranty data are limited by age and mileage. Age, as a function of time, is known for all sold vehicles at all time. However, mileage is only observed for a vehicle with at least one claim and only at the time of the claim. To deal with this problem of incomplete mileage information, we consider a linear approach and a piece-wise linear approach within a nonparametric framework. We explore the univariate case, as well as the bivariate case. For the univariate case, we evaluate the mean cumulative warranty cost and its standard error as a function of age, a function of mileage, and a function of actual (calendar) time. For the bivariate case, we evaluate the mean cumulative warranty cost as a function of age and mileage. The effect of reporting delay of claim and several methods for making prediction are also considered. Throughout this thesis, we illustrate the ideas using examples based on real data.</p>

Data Mining in Automotive Warranty Analysis

<p>This thesis is about data mining in automotive warranty analysis, with an emphasis on modeling the mean cumulative warranty cost or number of claims (per vehicle). In our study, we deal with a type of truncation that is typical for automotive warranty data, where the warranty coverage and the resulting warranty data are limited by age and mileage. Age, as a function of time, is known for all sold vehicles at all time. However, mileage is only observed for a vehicle with at least one claim and only at the time of the claim. To deal with this problem of incomplete mileage information, we consider a linear approach and a piece-wise linear approach within a nonparametric framework. We explore the univariate case, as well as the bivariate case. For the univariate case, we evaluate the mean cumulative warranty cost and its standard error as a function of age, a function of mileage, and a function of actual (calendar) time. For the bivariate case, we evaluate the mean cumulative warranty cost as a function of age and mileage. The effect of reporting delay of claim and several methods for making prediction are also considered. Throughout this thesis, we illustrate the ideas using examples based on real data.</p>

Approximation of random functions by stochastic Bernstein polynomials in capacity spaces

Given a submodular capacity space, we firstly obtain a quantitative estimate for the uniform convergence in the Choquet p-mean, 1\le p<\infty, of the multivariate stochastic Bernstein polynomials associated to a random function. Also, quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

Slopes of links and signature formulas

We present a new invariant, called slope, of a colored link in an integral homology sphere and use this invariant to complete the signature formula for the splice of two links. We develop a number of ways of computing the slope and a few vanishing results. Besides, we discuss the concordance invariance of the slope and establish its close relation to the Conway polynomials, on the one hand, and to the Kojima–Yamasaki η \eta -function (in the univariate case) and Cochran invariants, on the other hand.

Approximative characteristics of the Nikol'skii-Besov-type classes of periodic functions in the space $B_{\infty,1}$

We obtained the exact order estimates of the orthowidths and similar to them approximative characteristics of the Nikol'skii-Besov-type classes $B^{\Omega}_{p,\theta}$ of periodic functions of one and several variables in the space $B_{\infty,1}$. We observe, that in the multivariate case $(d\geq2)$ the orders of orthowidths of the considered functional classes are realized by their approximations by step hyperbolic Fourier sums that contain the necessary number of harmonics. In the univariate case, an optimal in the sense of order estimates for orthowidths of the corresponding functional classes there are the ordinary partial sums of their Fourier series. Besides, we note that in the univariate case the estimates of the considered approximative characteristics do not depend on the parameter $\theta$. In addition, it is established that the norms of linear operators that realize the order of the best approximation of the classes $B^{\Omega}_{p,\theta}$ in the space $B_{\infty,1}$ in the multivariate case are unbounded.

Linear and Kolmogorov widths of the classes B^{\Omega}_{p, \theta} of periodic functions of one and several variables

Some estimates exact in order for linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic multivariable functions in the space $L_q$ with certain relations between the parameters $p$, $q,$ and $\theta$ are obtained. In the univariate case, the estimates exact in order for Kolmogorov and linear widths of the classes $B^{\omega}_{\infty, \theta}$ in the space $L_q$, $1 \leq q \leq \infty,$ are established.

Asymptotics of Bivariate Analytic Functions with Algebraic Singularities

International audience In this paper, we use the multivariate analytic techniques of Pemantle and Wilson to find asymptotic for- mulae for the coefficients of a broad class of multivariate generating functions with algebraic singularities. Flajolet and Odlyzko (1990) analyzed the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by immediately reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new multivariate analytic techniques and used them to analyze the coefficients of rational generating functions.

Bayesian Inference for Skew-Symmetric Distributions

Skew-symmetric distributions are a popular family of flexible distributions that conveniently model non-normal features such as skewness, kurtosis and multimodality. Unfortunately, their frequentist inference poses several difficulties, which may be adequately addressed by means of a Bayesian approach. This paper reviews the main prior distributions proposed for the parameters of skew-symmetric distributions, with special emphasis on the skew-normal and the skew-t distributions which are the most prominent skew-symmetric models. The paper focuses on the univariate case in the absence of covariates, but more general models are also discussed.