Estimation of the failure rate-a survey of nonparametric methods Part I: Non-Bayesian Methods

In this paper several nonparametric, non-Bayesian methods for estimating the failure rate function on which no monotonicity conditions have been imposed are surveyed. The survey attempts to consolidate and synthesize literature from several diverse areas of application, and endeavors to be as up-to-date as is feasible.

[1]  Fourier Integral Estimate of the Failure Rate Function and Its Mean Square Error Properties , 1982 .

[2]  Nozer D. Singpurwalla,et al.  Large Sample Estimates and Uniform Confidence Bounds for the Failure Rate Function Based on a Naive Estimator , 1981 .

[3]  F. Downton,et al.  Statistical analysis of reliability and life-testing models : theory and methods , 1992 .

[4]  E. Wegman,et al.  A time series approach to life table construction , 1980 .

[5]  Jon A. Wellner,et al.  Confidence bands for a survival curve from censored data , 1980 .

[6]  An estimator for the generalized hazard rate function , 1979 .

[7]  R. Tapia,et al.  Nonparametric Probability Density Estimation , 1978 .

[8]  A. V. Peterson.  Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions , 1977 .

[9]  I. Ahmad,et al.  Nonparametric Estimation of a Vector-Valued Bivariate Failure Rate , 1977 .

[10]  Nozer D. Singpurwalla,et al.  Failure Rate Estimation Using Random Smoothing. , 1977 .

[11]  M. Rosenblatt,et al.  On the Maximal Deviation of $k$-Dimensional Density Estimates , 1976 .

[12]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[13]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[14]  I. Ahmad.  UNIFORM STRONG CONVERGENCE OF A GENERALIZED FAILURE RATE ESTIMATE , 1976 .

[15]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[16]  R. E. Barlow,et al.  Total time on test processes and applications to failure data , 1975 .

[17]  P. Major,et al.  An approximation of partial sums of independent RV'-s, and the sample DF. I , 1975 .

[18]  J. Kalbfleisch.  Statistical Inference Under Order Restrictions , 1975 .

[19]  N. Breslow,et al.  A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship , 1974 .

[20]  Rupert G. Miller.  The jackknife-a review , 1974 .

[21]  P. Bickel,et al.  On Some Global Measures of the Deviations of Density Function Estimates , 1973 .

[22]  W. Strawderman.  The Generalized Jackknife Statistic , 1973 .

[23]  M. Woodroofe.  On Choosing a Delta-Sequence , 1970 .

[24]  B. Rao.  Estimation for distributions with monotone failure rate , 1970 .

[25]  W. V. Zwet,et al.  COMPARISON OF SEVERAL NONPARAMETRIC ESTIMATORS OF THE FAILURE RATE FUNCTION , 1969 .

[26]  S. Arunkumar.  ESTIMATION OF THE CHANGE POINT OF THE GENERALIZED FAILURE RATE FUNCTION , 1969 .

[27]  ASYMPTOTIC PROPERTIES OF ISOTONIC ESTIMATORS FOR THE GENERALIZED FAILURE RATE FUNCTION. PART II. ASYMPTOTIC DISTRIBUTIONS. , 1969 .

[28]  Richard E. Barlow,et al.  A Note on Tests for Monotone Failure Rate Based on Incomplete Data , 1969 .

[29]  E. Gehan.  Estimating survival functions from the life table. , 1969, Journal of chronic diseases.

[30]  V. K. Murthy.  Estimation of Jumps, Reliability and Hazard Rate , 1965 .

[31]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[32]  Frank Proschan,et al.  Maximum Likelihood Estimation for Distributions with Monotone Failure Rate , 1965 .

[33]  M. R. Leadbetter,et al.  HAZARD ANALYSIS II , 1964 .

[34]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[35]  A. W. Kimball,et al.  ESTIMATION OF MORTALITY INTENSITIES IN ANIMAL EXPERIMENTS , 1960 .

[36]  F. Ederer,et al.  Maximum utilization of the life table method in analyzing survival. , 1958, Journal of chronic diseases.

[37]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[38]  M. Rosenblatt.  Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[39]  G. Sacher.  On the statistical nature of mortality, with especial reference to chronic radiation mortality. , 1956, Radiology.

[40]  U. Grenander.  On the theory of mortality measurement , 1956 .

[41]  H. Seal.  The estimation of mortality and other decremental probabilities , 1954 .

[42]  J BERKSON,et al.  Calculation of survival rates for cancer. , 1950, Proceedings of the staff meetings. Mayo Clinic.