Data-Based Nonparametric Estimation of the Hazard Function with Applications to Model Diagnostics and Exploratory Analysis

The systematic risk estimation models: A different perspective

There is a long-standing debate in the statistical, epidemiological, and econometric fields as to whether nonparametric estimation that uses machine learning in model fitting confers any meaningful advantage over simpler, parametric approaches in finite sample estimation of causal effects. We address the question: when estimating the effect of a treatment on an outcome, how much does the choice of nonparametric vs parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach to compare estimators across a large number of data-generating mechanisms drawn from nonparametric models with semi-informative priors. We apply this proposed approach and compare the performance of two nonparametric estimators (Bayesian adaptive regression tree and a targeted minimum loss-based estimator) to two parametric estimators (a logistic regression-based plug-in estimator and a propensity score estimator) in terms of estimating the average treatment effect across thousands of data-generating mechanisms. We summarize performance in terms of bias, confidence interval coverage, and mean squared error. We find that the two nonparametric estimators can substantially reduce bias as compared to the two parametric estimators in large-sample settings characterized by interactions and nonlinearities while compromising very little in terms of performance even in simple, small-sample settings.

We consider the problem of choosing between two density estimates, a non-parametric estimate with the the standard properties of nonparametric estimates (universal consistency, robustness, but not extremely good rate of convergence) and a special estimate designed to perform well on a given set T of densities. The special estimate can often be thought of as a parametric estimate. The selection we propose is based upon the L1 distance oetween both estimates. Among otner things, we show how one should proceed to insure that the selected estimate matches the special estimate's rate on T, and that it matches the nonparametric estimate's rate off T

Process capability indices (PCIs) are widely used to assess whether an in-control process meets manufacturing specifications. In most applications of classical PCIs, the process characteristic is assumed normally distributed. However, the normal distribution has been found inappropriate in various applications. In the literature, the percentile-based PCIs are widely used to deal with the nonnormal process. One problem associated with the percentile-based PCIs is that they do not provide a quantitative interpretation to the process capability. In this study, new PCIs that have a consistent quantification to the process capability for both normal and nonnormal processes are proposed. The proposed PCIs are generalizations of the classical normal PCIs in the sense that they are the same as the classical PCIs when the process characteristic follows a normal distribution, and they offer the same interpretation to the process capability as the classical PCIs when the process characteristic is nonnormal. We then discuss nonparametric and parametric estimation of the proposed PCIs. The nonparametric estimator is based on the kernel density estimation and confidence limits are obtained by the nonparametric bootstrap, while the parametric estimator is based on the maximum likelihood estimation and confidence limits are constructed by the method of generalized pivots. The proposed methodologies are demonstrated using a real example from a manufacturing factory.

In this thesis, using a finance lens, we investigate various aspects of political actions of the Chinese National Social Security Fund (CNSSF). The thesis comprises three empirical papers. In the first essay, we analyze the trading behavior of the CNSSF that operates in a highly political environment. We show that the CNSSF adopts a rebalancing strategy that maintains both portfolio liquidity and growth opportunities. Further, we find direct and indirect evidence that the CNSSF actively intervenes in the stock market by providing liquidity to mutual funds in distress. This liquidity provision can be primarily explained by public information quality. Most notably, CNSSF can profit by assisting distressed mutual funds, especially if such liquidity provision relates to private information. In addition, this bailout-like behavior is not speculative and can positively improve the performance of the distressed mutual funds. In essay 2, we propose a new measure of the policy information advantage available to the CNSSF. Specifically, we assess the impact of this policy-linked “information advantage” on stock performance. Our results show that in the short run, there is a positive and significant information advantage-stock performance linkage. Moreover, our findings support the view that CNSSF promotes the absorption of inside information into prices. In contrast, in the long run, the policy information advantage of the CNSSF negatively decreases the firm operation performance. Finally, we document that there is an information network spillover of the information advantage across the Chinese mutual fund industry, which also affects mutual fund performance. In the third essay, we propose a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using the CNSSF strategic stocks. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method.

In this paper, we adopt a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using China National Social Security Fund strategic stocks and Shanghai Stock Exchange 50 Index components.

Uno de los principales objetivos del área de confiabilidad es estimar la función de confiabilidad, donde tradicionalmente se utilizan estimadores no paramétricos, que son más eficientes en tamaños de muestras considerables. En este trabajo se comparan los estimadores no paramétricos para la función de confiabilidad a través del error cuadrático medio, utilizando los estimadores no paramétricos de Kaplan y Meier (1958), el estimador de Nelson (1969) y Bootstrap aplicado a Kaplan y Meier y Nelson. La comparación se hace teniendo en cuenta las estimaciones paramétricas, mediante simulación con diferentes escenarios, tiempos de interés, tamaños de muestra y porcentajes de censura, y muestra que el remuestreo Bootstrap tipo normal no presenta los mejores resultados con Kaplan y Meier (1958). Y mediante Nelson (1969), el 18 % fue más eficiente.

SUMMARY A great deal of recent attention has focused on the estimation of survival distributions based on current status data, an extreme form of interval censored data. This particular data structure arises in a wide variety of applications where cross-sectional observation either naturally occurs or is preferred to more traditional forms of follow-up. Here we consider current status data in the context of competing risks. We briefly consider simple parametric models as a backdrop to nonparametric procedures. We make some brief comparisons and remarks regarding the nonparametric maximum likelihood estimator. The ideas are illustrated on the data of Krailo & Pike (1983) which considers estimation of the age distribution at both natural and operative menopause. We also consider the case where there is exact observation of failure times due to one of the competing risks when failure occurs prior to the monitoring time. Basic techniques of survival analysis focus on estimation of the survival distribution based on various forms of censored data. An extreme form of censoring arises where the only information on studied individuals is their survival status at a single monitoring time. This particular data structure is known as current status data. Nonparametric estimation of the survival function and semiparametric techniques for related regression models, based on current status data, have been much studied of late. Here, we consider estimation of sub-survival functions based on current status observations in the presence of competing risks. For simplicity, we describe only two competing risks, but the ideas are easily extended when there are more than two possible causes of failure. Let )j denote the cause-specific hazard function for cause j = 1, 2 (Kalbfleisch & Prentice, 2002, p. 252). If T and J are the random variables that measure time to failure and cause of failure, respectively, the two sub-distribution functions of interest are

A well known category of classification error rate estimators is so called parametric error rate estimators. These estimators are typically expressed as functions of the training sample size, the dimensionality of the observation vector and the Mahalanobis distance between the classes. However, all parametric classification error rate estimators are biased and the main source of this bias is the estimate of the Mahalanobis distance. In this paper we propose a new Mahalanobis distance estimation method that is designed for use in parametric classification error rate estimators. Experiments with real world and synthetic data sets show that new estimator helps to reduce the bias of the most common parametric classification error rate estimators. Additionally, non-parametric classification error rate estimators, such as resubstitution, repeated 10-fold cross-validation and leave-one-out are outperformed (in terms of root-mean-square error) by parametric estimators that use new estimates of the Mahalanobis distance.

In regression analysis, a parametric model is often assumed from prior information or a pilot study. If the model assumption is valid, the parametric method is useful. However, the efficiency of the estimator is not guaranteed when a poor model is selected. This article aims to check whether the model assumption is correct or not and to estimate the regression function. To achieve this, we propose a hybrid technique of parametrically guided method and group lasso. First, the parametric model is prepared. The parametrically guided estimator is constructed by summing the parametric estimator and nonparametric estimator. For the estimation of the nonparametric component, we use B‐splines and the group lasso method. If the nonparametric component is estimated to be a zero function, the parametrically guided estimator is reduced to the parametric estimator. Then, we can decide that the parametric model assumption is correct. If the nonparametric estimator is not zero, the semiparametric estimator is obtained. Thus, the proposed method discovers the model structure and estimates the regression function simultaneously. We investigate the asymptotic properties of the proposed estimator. A simulation study and real data example are presented. Copyright © 2016 John Wiley & Sons, Ltd.

In the present paper we generalise the classical newsvendor problem for critical perishable commodities having more severe costs than its linear alternative. Piece wise polynomial cost functions are introduced to accommodate the excess severity. Stochastic demand is assumed to follow a completely unknown probability distribution. Non parametric estimator of the optimal order quantity has been developed from an estimating equation using a random sample. Strong consistency of the estimator is proved for unique optimal order quantity and the result is extended for multiple solutions. Simulation results indicate that non parametric estimator is efficient in terms of mean square error. Real life application of the proposed non-parametric estimator has been demonstrated with Avocado demand in the United States of America and Covid-19 test kit demand during second wave of SARS-COV2 pandemic across 86 countries.

In the problem of estimating an unknown distribution function $F$ in the presence of censoring, one can use a nonparametric estimator such as the Kaplan-Meier estimator, or one can consider parametric modeling. There are many situations where physical reasons indicate that a certain parametric model holds approximately. In these cases a nonparametric estimator may be very inefficient relative to a parametric estimator. On the other hand, if the parametric model is only a crude approximation to the actual model, then the parametric estimator may perform poorly relative to the nonparametric estimator, and may even be inconsistent. The Bayesian paradigm provides a reasonable framework for this problem. In a Bayesian approach, one would try to put a prior distribution on $F$ that gives most of its mass to small neighborhoods of the entire parametric family. We show that certain priors based on the Dirichlet process prior can be used to accomplish this. For these priors the posterior distribution of $F$ given the censored data appears to be analytically intractable. We provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm. We also show convergence of the algorithm.

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach.The Canadian Journal of Statistics47: 668–687; 2019 © 2019 Statistical Society of Canada

We study the parameter estimation for ergodic diffusion process Xt from perturbed observations where are observation times and the noise is a strongly mixing stationary noisy process with the density function g. We construct an estimator of the diffusion parameters based on the minimum Hellinger distance between the density of the invariant distribution of diffusion process Xt and the nonparametric deconvolution kernel estimator of this density. This article focuses on the ordinary smooth noise density class with the assumption (where and is characteristic function of noisy random variable). This assumption is more general than the condition (where C is a constant) which is used in a lot of articles. We also discuss the asymptotic normality for both the estimator of deconvolution kernel density and the estimator of diffusion parameters. Finally, we illustrate the properties of the estimator by two examples of diffusion processes.

In this paper, the synthetic aperture radar tomography (SARTom) vertical distribution estimation problem is treated within the direction of arrival (DOA) estimation framework. Super-resolution parametric DOA estimation methods improve the vertical resolution and mitigate the effect of sidelobes. Nevertheless, these techniques have the main drawback related to the assumption that the scene is composed by a finite number of point-type backscattering sources. On the other hand, the minimum variance distortionless response (MVDR) inspired non-parametric DOA estimation methods are better suited to cope with scenarios characterized by the presence of distributed scatterers. In this work, we propose to decompose the SARTom vertical distribution estimation problem into two paradigms: parametric DOA estimation for point-type scatterers and non-parametric recovery of the spatial spectrum pattern (SSP) of the spatially distributed scattering components. The principal innovative contribution of this study relates to the proposition for fusion of the Prony-inspired parametric and MVDRinspired non-parametric DOA estimation paradigms through the use of the spectral positional invariance property of the point-type targets, which holds with the extended Prony model.