arXiv subjects

Budhi Surya

Publications and source records attributed to Budhi Surya.

9 recordsLinked to original sources

arXiv2026

Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data

Phase-type (PH) distributions are versatile semi-parametric models for lifetime duration and can be used in survival and reliability analysis. In this paper we put forward methods and software for using PH distributions in a competing-risks model. The resulting multi-absorbing phase-type (MAPH) distribution records both the time until absorption and its cause. After formulating basic properties of this family, we develop an EM algorithm for parameter inference from exact event-time/cause observations and independently right-censored observations. For a censored subject, the E-step conditions on survival up to the censoring time and imputes both the latent transient path and its eventual cause of absorption; closed-form cause-resolved sufficient-statistic expectations are obtained from matrix exponentials. We illustrate applications and numerical properties and describe two accompanying Julia packages, in which both the exact-event and the censored E-step are implemented. Applied to intensive-care length-of-stay data in full, censored records included, the method attains a higher likelihood than the phase-type competing-risks fit previously published for those data.

stat.ME↗

arXiv2022

Statistical inference for a mixture of Markov jump processes

We estimate a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the transition intensity matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The new mixture is estimated from its continuously observed realizations using the EM algorithm, which provides the maximum likelihood (ML) estimates of the mixture's parameters. We derive the asymptotic properties of the ML estimators. To obtain estimated standard errors of the ML estimates of the mixture's parameters, an explicit form of the observed Fisher information matrix is derived. In its new form, the information matrix simplifies the conditional expectation of outer product of the complete-data score function in the Louis (1982) general matrix formula for the observed Fisher information matrix. Simulation study verifies the estimates' accuracy and confirms the consistency and asymptotic normality of the estimators. The developed methods are applied to a medical dataset, for which the likelihood ratio test rejects the constrained mixture in favor of the proposed unconstrained one. This application exemplifies the usefulness of a new unconstrained mixture for identification and characterization of homogeneous subpopulations in a heterogeneous population.

stat.ME↗

arXiv2021

A new class of conditional Markov jump processes with regime switching and path dependence: properties and maximum likelihood estimation

This paper develops a new class of conditional Markov jump processes with regime switching and paths dependence. The key novel feature of the developed process lies on its ability to switch the transition rate as it moves from one state to another with switching probability depending on the current state and time of the process as well as its past trajectories. As such, the transition from current state to another depends on the holding time of the process in the state. Distributional properties of the process are given explicitly in terms of the speed regimes represented by a finite number of different transition matrices, the probabilities of selecting regime membership within each state, and past realization of the process. In particular, it has distributional equivalent stochastic representation with a general mixture of Markov jump processes introduced in Frydman and Surya (2020). Maximum likelihood estimates (MLE) of the distribution parameters of the process are derived in closed form. The estimation is done iteratively using the EM algorithm. Akaike information criterion is used to assess the goodness-of-fit of the selected model. An explicit observed Fisher information matrix of the MLE is derived for the calculation of standard errors of the MLE. The information matrix takes on a simplified form of the general matrix formula of Louis (1982). Large sample properties of the MLE are presented. In particular, the covariance matrix for the MLE of transition rates is equal to the Cramér-Rao lower bound, and is less for the MLE of regime membership. The simulation study confirms these findings and shows that the parameter estimates are accurate, consistent, and have asymptotic normality as the sample size increases.

stat.ME↗

arXiv2021

Efficient Estimation For The Joint Model of Survival and Longitudinal Data

In survival studies it is important to record the values of key longitudinal covariates until the occurrence of event of a subject. For this reason, it is essential to study the association between longitudinal and time-to-event outcomes using the joint model. In this paper, profile likelihood approach has been used to estimate the cumulative hazard and regression parameters from the joint model of survival and longitudinal data. Moreover, we show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator. The estimators of the regression parameters from the joint model are shown to be semi-parametric efficient.

stat.ME↗

arXiv2020

A Two-Phase Dynamic Contagion Model for COVID-19

In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process(2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao (2011). It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and countries. The associated time lag of the effect of intervention in each country or region is estimated. Our results are consistent with the incubation time of COVID-19 found by recent medical study. We demonstrate that our model could potentially be a valuable tool in the modeling of COVID-19. More importantly, the proposed model of 2P-DCP could also be used as an important tool in epidemiological modelling as this type of contagion models with very simple structures is adequate to describe the evolution of regional epidemic and worldwide pandemic.

physics.soc-ph↗

arXiv2020

Parisian excursion with capital injection for draw-down reflected Levy insurance risk process

This paper discusses Parisian ruin problem with capital injection for Levy insurance risk process. Capital injection takes place at the draw-down time of the surplus process when it drops below a pre-specified function of its last record maximum. The capital is continuously paid to keep the surplus above the draw-down level until either the surplus process goes above the record high or a Parisian type ruin occurs, which is announced at the first instance the surplus process has undergone an excursion below the record for an independent exponential period of time consecutively since the time the capital was first injected. Some distributional identities concerning the excursion are presented. Firstly, we give the Parisian ruin probability and the joint Laplace transform (possibly killed at the first passage time above a fixed level of the surplus process) of the ruin time, surplus position at ruin, and the total capital injection at ruin. Secondly, we obtain the $q$-potential measure of the surplus process killed at Parisian ruin. Finally, we give expected present value of the total discounted capital payments up to the Parisian ruin time. The results are derived using recent developments in fluctuation and excursion theory of spectrally negative Levy process and are presented semi explicitly in terms of the scale function of the Levy process. Some numerical examples are given to facilitate the analysis of the impact of initial surplus and frequency of observation period to the ruin probability and to the expected total capital injection.

q-fin.MF↗

arXiv2020

Optimal valuation of American callable credit default swaps under drawdown of Lévy insurance risk process

This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in favour of the buyer as she only pays the premium when the market is in good condition for the protection against financial downturn. Under this framework, we look at an embedded option which gives the issuer an opportunity to call back the contract to a new one with reduced premium payment rate and slightly lower default coverage subject to paying a certain cost. We assume that the buyer is risk neutral investor trying to maximize the expected monetary value of the option over a class of stopping time. We discuss optimal solution to the stopping problem when the source of uncertainty of the asset price is modelled by Lévy process with only downward jumps. Using recent development in excursion theory of Lévy process, the results are given explicitly in terms of scale function of the Lévy process. Furthermore, the value function of the stopping problem is shown to satisfy continuous and smooth pasting conditions regardless of regularity of the sample paths of the Lévy process. Optimality and uniqueness of the solution are established using martingale approach for drawdown process and convexity of the scale function under Esscher transform of measure. Some numerical examples are discussed to illustrate the main results.

q-fin.MF↗

arXiv2020

Efficient Estimation For The Cox Proportional Hazards Cure Model

While analysing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using cure model which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package (Cai et al., 2012) and we compare the results with the output obtained from SMCURE package.

stat.ME↗

arXiv2017

Discounted Penalty Function at Parisian Ruin for Lévy Insurance Risk Process

In the setting of a Lévy insurance risk process, we present some results regarding the Parisian ruin problem which concerns the occurrence of an excursion below zero of duration bigger than a given threshold $r$. First, we give the joint Laplace transform of ruin-time and ruin-position (possibly killed at the first-passage time above a fixed level $b$), which generalises known results concerning Parisian ruin. This identity can be used to compute the expected discounted penalty function via Laplace inversion. Second, we obtain the $q$-potential measure of the process killed at Parisian ruin. The results have semi-explicit expressions in terms of the $q$-scale function and the distribution of the Lévy process.

math.PR↗