How to replace 'for' loop by 'xarray.apply_ufunc' to performing linear regression between "x" and "y" for a 11-day moving-window for a xr.Dataset?

I want to estimate the linear slope between ‘x’ and ‘y’ for each 11-day moving window by 1-day stride.

from sklearn import linear_model
import numpy as np
import xarray as xr
import pandas as pd

# Create a dataset as an example
site = np.linspace(0,3,dtype='int8')
time= pd.date_range('2018-01-01','2020-12-31',freq='d')
x = np.random.randint(0,500,size=[len(site), len(time)])
y = np.random.randint(0,500,size=[len(site), len(time)])

_ds = xr.Dataset(data_vars=dict(
                    x=(["site", "time"], x),
                    y=(["site", "time"], y)),

# define the linear regression model
def ransac_fit(xi,yi, **ransac_kwargs):
    Xi = xi.reshape(-1, 1)
    yi = yi
    ransac = linear_model.RANSACRegressor(**ransac_kwargs), yi)
    slope= ransac.estimator_.coef_
    b = ransac.estimator_.intercept_
    return slope, b

At present I am able to use ‘for’ loop for ‘site’ and ‘time’ to do that, which however is extremely clumsy…

def clc_slope(_ds, window_size=11):
    slps    =[]
    bs      =[]
    mean_xs =[]
    var_x = _ds['x']
    var_y = _ds['y']
   # for loop for each year and date
    for year in np.unique(_ds.time.dt.year.values):
        for doy in np.unique(_ds.sel(time=str(year)).time.dt.dayofyear.values):
            # define inorg and endrg
            inorg =
            enorg =
            # calculate mean values of x and y for each moving window
            mean_x = np.nanmean(var_x.sel(time=str(year))[inorg:enorg].values)
            mean_y  = np.nanmean(var_y.sel(time=str(year))[inorg:enorg].values)
            mean_xs = np.append(mean_xs, mean_x)
            mean_ys  = np.append(mean_ys, mean_x)

            # start to estimate slope and intercept
            _x = var_x.sel(time=str(year))[inorg:enorg].values
            _y = var_y.sel(time=str(year))[inorg:enorg].values
            # if there is too many nans then assign slope and intcept to be nan
            if (np.isfinite(_x) & np.isfinite(_y)).sum()<((*1):
                _slp=_b= np.nan
                    _slp, _b = ransac_fit(_x,_y, min_samples=0.6,*1)
                    _slp=_b = np.nan

            slps = np.append(slps,_slp)
            bs   = np.append(bs, _b)

    outs = [slps, bs, mean_xs, mean_ys]
    return outs

# run the slope and intercept estimation for each site and concat afterwards
_dss = []
for st in
    _ds = ds.sel(site=st)
    outs = clc_slope(_ds)
    _ds['slp']    = ('time',outs[0])
    _ds['b']      = ('time',outs[1])
    _ds['mean_xs']= ('time',outs[2])
    _ds['mean_ys']= ('time',outs[3])
dss = xr.concat(_dss, dim='site')

I know xarray.apply_ufunc can extremely save time, but I do not get this tricky approach. Would be supper appreciate if you can give a hint! Thank you a million…