DeepAI AI Chat
Log In Sign Up

Adaptive estimation in symmetric location model under log-concavity constraint

by   Nilanjana Laha, et al.

We revisit the problem of estimating the center of symmetry θ of an unknown symmetric density f. Although stone (1975), Eden (1970), and Sacks (1975) constructed adaptive estimators of θ in this model, their estimators depend on external tuning parameters. In an effort to reduce the burden of tuning parameters, we impose an additional restriction of log-concavity on f. We construct truncated one-step estimators which are adaptive under the log-concavity assumption. Our simulations suggest that the untruncated version of the one step estimator, which is tuning parameter free, is also asymptotically efficient. We also study the maximum likelihood estimator (MLE) of θ in the shape-restricted model.


page 1

page 2

page 3

page 4


Location estimation for symmetric log-concave densities

We revisit the problem of estimating the center of symmetry θ of an unkn...

Estimating the scale parameters of several exponential distributions under order restriction

In the present work, we have investigated the problem of estimating para...

Adaptive and non-adaptive estimation for degenerate diffusion processes

We discuss parametric estimation of a degenerate diffusion system from t...

Unit-log-symmetric models: Characterization, statistical properties and its use in analyzing internet access data

We present here a unit-log-symmetric model based on the bivariate log-sy...

The Goldenshluger-Lepski Method for Constrained Least-Squares Estimators over RKHSs

We study an adaptive estimation procedure called the Goldenshluger-Lepsk...

Improved inference for vaccine-induced immune responses via shape-constrained methods

We study the performance of shape-constrained methods for evaluating imm...

Hidden Ergodic Ornstein-Uhlenbeck Process and Adaptive Filter

The model of partially observed linear stochastic differential equations...