Optimal Information Processing and Bayes's Theorem

In this article statistical inference is viewed as information processing involving input information and output information. After introducing information measures for the input and output information, an information criterion functional is formulated and optimized to obtain an optimal information processing rule (IPR). For the particular information measures and criterion functional adopted, it is shown that Bayes's theorem is the optimal IPR. This optimal IPR is shown to be 100% efficient in the sense that its use leads to the output information being exactly equal to the given input information. Also, the analysis links Bayes's theorem to maximum-entropy considerations.     

A new estimator of entropy

Vasicek (1976) proposed an estimator of entropy based on spacings. A new estimator of entropy is proposed. This new estimator is based on local linear regression. Comparisons between this new estimator and Vasicek's estimator are made. The mean square error (MSE) of the new estimator is consistently smaller than the MSE of Vasicek's estimator.     

Measures of dependence for the multivariate t distribution with applications to the stock market

Two measures of dependence for multivariate t and Cauchy random variables are developed based on Kullback–Leibler number. The mutual information number T(X) is obtained in a closed expression form, as well as its asymptotic distribution. A dependence coefficient ρ₁, is defined (based on the Kullback–Leibler number) with the properties of ρ₁=0 indicating independence and ρ₁=1indicating degeneracy. Two real life examples from the stock market are used to analyze the level of dependence and correlation among stocks.     

Confidence Intervals for Gini's Diversity Measure and Shannon's Entropy Using Adjusted Proportions

Abstract

Asymptotic confidence intervals are given for two functions of multinomial outcome probabilities: Gini's diversity measure and Shannon's entropy. “Adjusted” proportions are used in all asymptotic mean and variance formulas, along with a possible logarithmic transformation. Exact confidence coefficients are computed in some cases. Monte Carlo simulation is used in other cases to compare actual coverages to nominal ones. Some recommendations are made.     

Multivariate Measures of Well-Being and an Analysis of Inequality in the Michigan Data

We demonstrate a multidimensional approach for combining several indicators of well-being, including the traditional money-income indicators. This methodology avoids the difficult and much criticized task of computing imputed incomes for such indicators as net worth and schooling. Inequality in the proposed composite measures is computed using relative inequality indexes that permit simple analysis of both the contribution of each welfare indicator (and its factor components) and within and between components of total inequality when the population is grouped by income levels, age, gender, or any other criteria. The analysis is performed on U.S. data using the Michigan Survey of Income Dynamics.     

An extension of bayesian measure of information to regression

This paper extends Lindley's measure of average information to the linear model, E(Y∣ß) = Xß. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters ß will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.     

Estimation of signal to noise ratio using mahalanobis distance

In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

Renyi's entropy for residual lifetime distribution

In the present paper, we introduce and study Renyi's information measure (entropy) for residual lifetime distributions. It is shown that the proposed measure uniquely determines the distribution. We present characterizations for some lifetime models. Further, we define two new classes of life distributions based on this measure. Various properties of these classes are also given.