Maximum entropy in the mean methods in propensity score matching for interval and noisy data

Abstract

In this paper, we propose maximum entropy in the mean methods for propensity score matching classification problems. We provide a new methodological approach and estimation algorithms to handle explicitly cases when data is available: (i) in interval form; (ii) with bounded measurement or observational errors; or (iii) both as intervals and with bounded errors. We show that entropy in the mean methods for these three cases generally outperform benchmark error-free approaches.     

A statistical model of tracking

A method is proposed to model individual patterns of growth over time by linear combinations of optimally chosen weighted orthogonal vectors. The goal is to distinguish individuals who track from nontrackers. Nontrackers are defined as those who follow different, usually more complex, growth patterns than trackers. Thus, nontrackers require more vectors than do trackers in modeling their longitudinal observations. A method of specifying the class-specific vectors and individual weights is demonstrated. When the proportion of nontrackers in the population is small, a modified form of the Akaike maximum entropy criterion is used to select the number of vectors appopriate for each person and also to classify each person into a tracking category. When the proportion of nontrackers is large, the modified Akaike criterion together with scatterplots of the growth curve weights are needed to distinguish trackers from nontrackers. The apprach is illustrated with longitudinal observations of height measured in an epidemiologic survey of children.     

On derivaton and application of aic as a data-based criterion for histograms

In this paper a derivation of the Akaike's Information Criterion (AIC) is presented to select the number of bins of a histogram given only the data, showing that AIC strikes a balance between the “bias” and “variance” of the histogram estimate. Consistency of the criterion is discussed, an asymptotically optimal histogram bin width for the criterion is derived and its relationship to penalized likelihood methods is shown. A formula relating the optimal number of bins for a sample and a sub-sample obtained from it is derived. A number of numerical examples are presented.     

On estimation of the scale matrix of the multivariate f distribution

Let F _p×phave a multivariate F distribution with a scale p×p matrix Δ and degrees of freedom k₁ and k₂ such that k_i - p - 1 > 0, i = 1,2. The estimation of Δ under entropy and squared error loss functions are considered. In both cases a new class of orthogonally invariant estimators are obtained which dominate the best unbiased estimator.     

Bayesian estimation of proportions with a cross-entropy prior

This paper suggests estimators of the frequencies (N₈) or proportions {N₈/N) of N distinguishable objects contained in S categories; given various types of information, We consider information in the form of exact constraints on the N₈, sample frequencies, and frequencies of related data, The analysis uses Bayesian methods, where the prior distribution is assumed to be a function of the cross-entropy between the N₈ and a reference distribution, We show the relationship between our estimator and the log-linear and logit models and also present a sampling experiment to compare our proposed estimator with the iterated proportional fitting estimator.     

Nonparametric estimation of the hazard function under dependence conditions

The estimation of the hazard rate has a great number of practical appli¬cations in dependence situations (seismicity analysis, reliability, economics), Based on kernel estimates of the density and the distribution function, we study the properties of the nonparametric estimator of the hazard function as-sociated with a strongly mixing time series. We prove consistency and asymp¬totic normality properties, and a cross-validation method for the smoothing parameter selection is studied. Some simulations and a practical application to real data are also shown.     

Entropy measures associated with j-divergences

This paper shows the different entropy measures which originate from the distance, in the sense of the J-divergences, between one distribution and the reference distribution.

Here are studied several conditions for the concavity and non-negativity of the proposed measure, and the reference distribution is characterized by the Dalton–Pielou condition.

At last, an interpretation of the and ψ-entropies is gotten, from the distance between one distribution and the equilibrium distribution.     

Reference prior bayes estimator for bivariate normal covariance matrix with risk comparison

The explicit form of the reference prior bayes estimator due to Yang and Ber-ger (1994) for bivariate normal covariance matrix under entropy loss is given in terms of Legendre polynomials when degrees of freedom is even and in terms of hypergeometric functions in general case. The finite series expression of the density function of the ratio of latent roots of bivariate Wishart matrix is obtained and the exact risk is compared with those of James-Stein minimax estimator and other orthogonally equivariant estimators. It is found numerically that the reference prior bayes estimator has the smallest risk among the class of equivariant estimators compared, when the ratio of the largest to the smallest population latent roots of covariance matrix lies in the middle of the interval [1, ∞]. It has larger risk than that of James-Stein minimax estimator when the ratio is large. Moreover it has larger risk than that of MLE when, for instance, degrees of freedom is 20 and the ratio lies between 4 and 8.     

CSISZAR DIVERGENCE FROM CONSTANT FAILURE RATE MODEL FOR GROUPED DATA

We propose a measure of divergence in failure rates of a system from the constant failure rate model for a grouped data situation. We use this measure to compare the divergences of several systems from the constant failure rate model and find the asymptotic distributions of the test statistics. Several applications are discussed to illustrate the procedure. In the context of testing the goodness-of-fit with the constant failure rate model, we conduct a simulation study which shows that this procedure compares favorably with the Pearson chi-square test and the likelihood ratio test procedures.