ESTIMATES OF DERIVATIVES OF (LOG) DENSITIES AND RELATED OBJECTS

We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density function f. The estimator is guaranteed to be non-negative and achieves the same optimal rate of convergence in the interior as on the boundary of the support of f. The estimator is therefore well-suited to applications in which non-negative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show that our estimator compares favorably with other kernel-based methods, both in terms of asymptotic performance and computational ease. Simulation results confirm that our method can perform similarly or better in finite samples compared to these alternative methods when they are used with optimal inputs, that is, an Epanechnikov kernel and optimally chosen bandwidth sequence. We provide code in several languages.

An Asymmetric Bimodal Double Regression Model

In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.

The asymptotic distribution of the Net Benefit estimator in presence of right-censoring

The benefit–risk balance is a critical information when evaluating a new treatment. The Net Benefit has been proposed as a metric for the benefit–risk assessment, and applied in oncology to simultaneously consider gains in survival and possible side effects of chemotherapies. With complete data, one can construct a U-statistic estimator for the Net Benefit and obtain its asymptotic distribution using standard results of the U-statistic theory. However, real data is often subject to right-censoring, e.g. patient drop-out in clinical trials. It is then possible to estimate the Net Benefit using a modified U-statistic, which involves the survival time. The latter can be seen as a nuisance parameter affecting the asymptotic distribution of the Net Benefit estimator. We present here how existing asymptotic results on U-statistics can be applied to estimate the distribution of the net benefit estimator, and assess their validity in finite samples. The methodology generalizes to other statistics obtained using generalized pairwise comparisons, such as the win ratio. It is implemented in the R package BuyseTest (version 2.3.0 and later) available on Comprehensive R Archive Network.

Subgraph Network Random Effects Error Components Models: Specification and Testing

This paper develops a subgraph random effects error components model for network data linear regression where the unit of observation is the node. In particular, it allows for link and triangle specific components, which serve as a basal model for modeling network effects. It then evaluates the potential effects of ignoring network effects in the estimation of the coefficients’ variance-covariance matrix. It also proposes consistent estimators of the variance components using quadratic forms and Lagrange Multiplier tests for evaluating the appropriate model of random components in networks. Monte Carlo simulations show that the tests have good performance in finite samples. It applies the proposed tests to the Call interbank market in Argentina.

COMPARING THE SMALL-SAMPLE ESTIMATION ERROR OF CONCEPTUALLY DIFFERENT RISK MEASURES

Motivated by the need to correctly rank risky alternatives in many investment, insurance and operations research applications, this paper uses a generalized location and scale framework from utility theory to propose a simple but powerful metric for comparing the estimation error of conceptually different risk measures. In an illustrative application, we obtain this metric — the probability that a risk measure ranks two assets falsely in finite samples — via Monte Carlo simulation for fourteen popular measures of risk and different distributional settings. Its results allow us to highlight interesting risk measure properties such as their relative quality under varying degrees of skewness and kurtosis. Because of the generality of our approach, the error probabilities derived for classic risk measures can serve as a benchmark for newly proposed measures seeking to replace the classic ones in decision making. It also supports the identification of the most suitable risk measures for a given distributional environment.

Bias-Corrected Maximum Likelihood Estimators of the Parameters of the Unit-Weibull Distribution

It is well known that the maximum likelihood estimates (MLEs) have appealing statistical properties. Under fairly mild conditions their asymptotic distribution is normal, and no other estimator has a smaller asymptotic variance.However, in finite samples the maximum likelihood estimates are often biased estimates and the bias disappears as the sample size grows.Mazucheli, Menezes, and Ghitany (2018b) introduced a two-parameter unit-Weibull distribution which is useful for modeling data on the unit interval, however its MLEs are biased in finite samples.In this paper, we adopt three approaches for bias reduction of the MLEs of the parameters of unit-Weibull distribution.The first approach is the analytical methodology suggested by Cox and Snell (1968), the second is based on parametric bootstrap resampling method, and the third is the preventive approach introduced by Firth (1993).The results from Monte Carlo simulations revealed that the biases of the estimates should not be ignored and the bias reduction approaches are equally efficient. However, the first approach is easier to implement.Finally, applications to two real data sets are presented for illustrative purposes.

Testing the proportionality assumption for specified covariate in the cox model

In this paper, I propose a test for proportional hazards assumption for specified covariates. The testis based on a general alternative in sense that hazards rates under different values of covariates therate is not only constant as in the Cox model, but it may cross, go away, and may be monotonicwith time. The limit distribution of the test statistic is derived. Finite samples properties of thetest power are analyzed by simulation. Application of the proposed test on Real data examples areconsidered.

The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.