Hypothesis testing and region estimation in non-linear regression

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A Rank Test on Equality of Population Medians

The Kruskal-Wallis test is a non-parametric test for the equality of K population medians. The test statistic involved is a measure of the overall closeness of the K average ranks in the individual samples to the average rank in the combined sample. The resulting acceptance region of the test however may not be the smallest region with the required acceptance probability under the null hypothesis. Presently an alternative acceptance region is constructed such that it has the smallest size, apart from having the required acceptance probability. Compared to the Kruskal-Wallis test, the alternative test is found to have larger average power computed from the powers along the evenly chosen directions of deviation of the medians

Prediction of the start of next recession

The future value of the binary recession variable is modeled to be dependent on the present and past values of a set of m US economic variables selected from a pool of 14 variables via a conditional distribution which is derived from an -dimensional power-normal distribution. The mean together with the 2.5% and 97.5% points of the conditional distribution are used to predict the start of the next US recession. When and , some of the models can provide fairly good indicators for the start of the next US recession

Estimation of transition probabilities of credit ratings for several companies

This paper attempts to estimate the transition probabilities of credit ratings for a number of companies whose ratings have a dependence structure. Binary codes are used to represent the index of a company together with its ratings in the present and next quarters. We initially fit the data on the vector of binary codes with a multivariate power-normal distribution. We next compute the multivariate conditional distribution for the binary codes of rating in the next quarter when the index of the company and binary codes of the company in the present quarter are given. From the conditional distribution, we compute the transition probabilities of the company’s credit ratings in two consecutive quarters. The resulting transition probabilities tally fairly well with the maximum likelihood estimates for the time-independent transition probabilities

Prediction of mortality rates using a model with stochastic parameters

Prediction of future mortality rates is crucial to insurance companies because they face longevity risks while providing retirement benefits to a population whose life expectancy is increasing. In the past literature, a time series model based on multivariate power-normal distribution has been applied on mortality data from the United States for the years 1933 till 2000 to forecast the future mortality rates for the years 2001 till 2010. In this paper, a more dynamic approach based on the multivariate time series will be proposed where the model uses stochastic parameters that vary with time. The resulting prediction intervals obtained using the model with stochastic parameters perform better because apart from having good ability in covering the observed future mortality rates, they also tend to have distinctly shorter interval lengths

Prediction of mortality rates using augmented data

Prediction of future mortality rate is of significant priority in the insurance industry today as insurers face challenging tasks in providing retirement benefits to a population with increasing life expectancy. A time series model based on multivariate power-normal distribution has been used in the literature on the United States (US) mortality data in the years 1933 to 2000 to predict the future mortality rates in the years 2001 to 2010. To improve the predictive ability, the US mortality data is augmented to include more variables such as death rates by gender and death rates of other countries with similar demographics. Apart from having good ability to cover the observed future mortality rate, the prediction intervals based on the augmented data performed better because they also tend to have shorter interval lengths

Prediction of reserves using multivariate power-normal mixture distribution

Recently, in the area on stochastic loss reserving, there are a number of papers which analyze the individual claims data using the Position Dependent Marked Poisson Process. The present paper instead uses a different type of individual data. For the i-th (1 ≤ i ≤ n) customer, these individual data include the sum insured i s together with the amount paid ij y and the amount ij a reported but not yet paid in the j-th (1 6) j dd development year. A technique based on multivariate power-normal mixture distribution is already available for predicting the future value ( 1 ijy � , 1 ija � ) using the present year value(,) i j i j ya and the sum insured i s . Presently the above technique is improved by the transformation of distribution which is defined on the whole real line to one which is non-negative and having approximately the same first four moments as the original distribution. It is found that, for the dataset considered in this paper, the improved method giveV a better estimate for the reserve when compared with the chain ladder reserve estimate. Furthermore, the method is expected to provide a fairly reliable value for the Provision of Risk Margin for Adverse Deviation (PRAD

Interval estimation in the presence of an outlier

Outliers are often ubiquitous in surveys that involve linear measurements. Knowing that the presence of such extreme points can grossly distort statistical analyses, most researchers are often tempted to conveniently eliminate them from the data set without much careful consideration. In this study, we investigate the performance of confidence intervals for the population mean under the various probabilities of outlier being caused by uncorrectable human errors. The sample under study is randomly generated and subscribed to a normal distribution, and it contains only one outlier at one of the two extreme ends

Mini-computer Fermat number transform and application to digital signal processing.

Source: Masters Abstracts International, Volume: 40-07, page: . Thesis (M.A.Sc.)--University of Windsor (Canada), 1979

Modelling and forecasting with financial duration data using non-linear model

The class of autoregressive conditional duration (ACD) models plays an important role in modelling the duration data in economics and finance. This paper presents a non-linear model to allow the first four moments of the duration to depend nonlinearly on past information variables. Theoretically the model is more general than the linear ACD model. The proposed model is fitted to the data given by the 3534 transaction durations of IBM stock on five consecutive trading days. The fitted model is found to be comparable to the Weibull ACD model in terms of the in-sample and out-of-sample mean squared prediction errors and mean absolute forecast deviations. In addition, the Diebold-Mariano test shows that there are no significant differences in forecast ability for all models