George Otieno Orwa

On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total

The precision of an estimator is at times discussed regarding the variance. Usually, the exact value of the variance is unknown. The discussion relies on unknown populace quantities. When a researcher obtains the survey data, an estimate of the variance can, therefore, be calculated. When survey results are presented, it is good practice to provide variance estimates for the estimator used in the study. The estimator of the variance can further be used to construct confidence interval, assuming that the sampling distribution of estimator is approximately normal. This study proposes estimation of standard error and confidence interval for a nonparametric regression estimator for a finite population using bootstrapping method. The idea behind bootstrapping is to carry out computations on the collected data. Computation activity assists in estimating the disparity of statistics that are themselves computed from the same data. The variance of the Nadaraya-Watson estimator is derived, based on bootstrap procedure. This operation has led to the derivation of confidence interval associated with Nadaraya-Watson estimator of the population total. A simulation study has been carried out. The overall conclusion is that the confidence interval associated with Nadaraya-Watson estimator is tighter than all the other estimators (Horvitz-Thompson estimator, Local linear estimator, and Ratio estimator).

Asymptotic Properties of the Markov Chain Model method of finding Markov chains Generators of Empirical Transition Matrices in Credit Ratings Applications

Credit quality changes need to be analysed from time to time. A good model for analysis needs to determine the Capital and reserves needed to support Credit Instruments portfolios as well as individual Credits. Conditions under which the Series method of finding Markov chains generators of Empirical Transition Matrices in Credit Ratings applications are identified in this article. Searching for valid Generators especially when a true generator does not exist and the properties of the series method is shown. Credit exposures Transition from one rating to another as well as Historical information are used to model estimation that pro- vide a description of Credit quality evolution probability. Time Homogeneous Markov Model specification is popularly used but it is only good in providing a description of portfolio risk changes in the short run hence restrictive in long run Credit processes. I propose a test which is simple and is of time homogeneity null hypothesis performed on all types of data reported often. The data used in the test is Sovereign debt, Municipal Bonds and Commercial paper. I find that transitions on municipal Bond ratings are described adequately for a period of up to five years. The Commercial paper assumes Markovian characteristics for a period of up to Six Months on a scale of 30 days transitions and the Sovereign debt transitions are described adequately by the Markov model using small data sample sizes.

Sarima Versus Time Lagged Feedforward Neural Networks in Forecasting Precipitation

The precipitation estimates are considered to be very important in economic planning. Major economic sectors highly depend on the precipitation levels. These sectors include agriculture, tourism, mining and transport. In Kenya, rainfall amount fluctuates with time hence depending on empirical observations while predicting is a hard task. Various statistical techniques have been used in forecasting precipitation. Among these techniques is Holt Winters procedures and SARIMA due to the seasonality effect. SARIMA model has been found to be effective in forecasting precipitation. The model has therefore been the most commonly used while precipitation forecasts are required. However, there is no any statistical research that has been carried out to test the effectiveness of neural networks in forecasting precipitation. This research hence considered forecasting precipitation using SARIMA and TLFN models. Box-Jenkins procedures of forecasting were used. Comparison of forecasts from the two techniques was done through the use of Mean Absolute Deviation (MAD), Mean Squared Deviation (MSD) and Mean Absolute Percentage Error (MAPE) in order to conclude which technique gives the better forecasts. Time Lagged Feed forward Neural Network model performed better than Seasonal Autoregressive Integrated Moving Average.